Explain how to find the zeros of the given polynomial: x3+3x2–x−3
What are the zeros?
Answers
Answer:
Step-by-step explanation:
The zero (root) of a function is any value of the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x-axis.
~~~~~~~~~
f(x) = x³ + 3x² - x - 3
f(-3) = ( - 3 )³ + 3( - 3 )² - ( - 3 ) - 3 = 0
f(-1) = ( - 1 )³ + 3( - 1 )² - ( - 1 ) - 3 = 0
f(1) = ( 1 )² + 3( 1 )² - ( 1 ) - 3 = 0
Answer:
The zeroes of the function are x = -3, x = -1, and x = 1.
Step-by-step explanation:
We are given a polynomial and asked to find the zeroes of the polynomial. Our given polynomial is:
[tex]x^3 + 3x^2 - x - 3[/tex]
The zeroes of a polynomial are the solutions or roots of the function. This is where if the line were graphed, the line would intersect the x-axis at those points (sometimes there will only be one).
This is a cubic polynomial. We can use a factoring technique referred to as grouping, which is most effective when factoring a trinomial with the only satisfaction met is: a > 1.
However, it can also be used when a > 1 is not true.
We can work with an example polynomial first and then work through solving the given polynomial.
An example polynomial would be:
[tex]10x^2 + 8x - 9 = 0[/tex]
In grouping, our main goal is to factor as quickly as possible. If you examine the polynomial, there is no common factor between 10x², 8x, or -9, so we cannot take out a GCF and need to use another factoring technique.
Since a > 1, we can instantly jump to using the grouping factoring technique.
Please note that the parent function for a quadratic is [tex]ax^2 + bx + c = 0[/tex].
To group:
We want to find the product of the terms a and c. So, with our example polynomial, a is 10, b is 8, and c is -9. Therefore, let's find the product of 10 and -9.Using ac, we will list all available factors. After doing this, we will find two factors of ac that will add up to give us b.These two factors are then substituted with b and c in the following parent equation: [tex]ax^2 + bx + cx + d[/tex].Finally, the equation is factored using parentheses in the following format: [tex](ax^2 + bx)(+ cx + d) = 0[/tex]After we group the function, we take the GCF out of both parentheses sets and write it as a coefficient to the remaining bit of the parentheses. The two GCFs are a set of terms and the remaining portion is the other set of terms.Let's use grouping to solve [tex]x^3 + 3x^2 - x - 3[/tex].
Because we already have four terms, we can skip steps one through three and go straight to step four.
[tex](x^3 + 3x^2)(-x - 3)[/tex]
Now, we need to take the GCF of both parentheses sets. Let's do this with our first set of terms.
You can divide x² out of both x³ and 3x², so x² is the GCF, leaving x and 3 behind.Then, we can also do this with our second set of terms.
There is a -1 implied in front of x, and there is no other common term between -x and -3, so -1 is our GCF, leaving x and 3 behind.Because our remaining terms for both sets match, we have grouped our polynomial correctly. Now, let's combine our GCFs into one term and list our common term as the second term.
[tex](x^2-1)(x+3)[/tex]
Now, we can break apart x² - 1 into more factors.
This is the difference of two squares. The formula for the difference of two squares is [tex](a^2-b^2)=(a+b)(a-b)[/tex]
Our perfect squares are every integer in the spectrum of numbers, so 1 is a perfect square. Therefore, x² becomes x and 1 becomes ±1.
Our new terms would therefore be [tex](x+1)(x-1)(x+3)[/tex].
Finally, to find zeroes of a function, x needs to equal something. Therefore, we can set our terms equal to zero and solve for x.
Term 1 (x + 1)
[tex]x + 1 = 0\\\\x + 1 - 1 = 0 - 1\\\\\boxed{x = -1}[/tex]
Term 2 (x - 1)
[tex]x - 1 = 0\\\\x - 1 + 1 = 0 + 1\\\\\boxed{x = 1}[/tex]
Term 3 (x + 3)
[tex]x + 3 = 0\\\\x + 3 - 3 = 0 - 3\\\\\boxed{x = -3}[/tex]
Therefore, our zeroes are listed above. To finalize our answer, we want to list them in increasing order, so this will be most negative to most positive. Therefore, our final answer is x = -3, -1, 1.
Related Questions
complete the equation of this line in slope-intercept form y= _x-1
Answers
Answer:
it will be 3 hope that helps
MARKING BRAINLIST!! A circular railroad crossing sign has a diameter of 40 inches. Which measurement is closest to the area of the sign in square inches?
A. 12.56 in
B. 62.8 in
C. 31.4 in.
D. 314 in.
Answers
Answer:
Step-by-step explanation:
Area of the circleis,
A=3.14 x r^2
d=40 in, r=20 in
A=20x20x3.14=400x3.14=1256 in^2
please help, would appreciate it!
Answers
Answer:
100 because it is corresponding angels ...
Step-by-step explanation:
because it is the same angle as ABC and you know BCD is 100
you need 180 degrees total
3(-5x+3)=8x+9 how do i find x?
Answers
Answer:
No solution
Step-by-step explanation:
-15x+9=8x+9
-23x=0
No solution
Answer:
x=0
Explanation:
3(−5x+3)=8x+9
x=0
Which is an equation of the line that passes through (2, –3) and (4, –7)?
Answers
AREA OF CIRCLE !! PLEASE HELP !! WILL GIVE BRAINLIEST !!
Answers
Answer:
A circle doesnt have a area its 0 duhhh
Step-by-step explanation:
PLEASEE ANSWER!! WILL GIVE 40 POINTS AND BRAINLIEST
Jessica loves the smell of candles in her home. She bought a candle, and it burns down at the rate of 0.5 inches per hour. The original height
of the candle was 9 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning
For example, the point (0.9) would represent a height of 9 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
(0.9),(__),(__),(__),(__),(__),(__)
Part B: Is this relation a function? Yes or no? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.45 inches per hour instead of 0.5 inches per hour, would the relation be a function? Yes or
no? Explain your answer using input and output values.
Answers
Step-by-step explanation:
Original height is the initial value, burn down rate is 0.5 inches per hour
This would be represented by a function:
y = 9 - 0.5xPart AOrdered pairs:
(0, 9), (1, 8.5), (2, 8), (3, 7.5), (4, 7), (5, 6.5), (6, 6)Part BRate of burn down is stable at 0.5 inches, this is a functionPart CIf the rate at which the candle burned was 0.45 inches per hour instead of 0.5 inches per hour, the relation would still be a function. The output values would have same difference of 0.45 inches and the function would be:
y = 9 - 0.45xFind the exterior angle measure:
Answers
Answer:
59 degrees
Step-by-step explanation:
The total amount of degrees for a triangle must add up to 180 degrees.
74 + 47 = 121
180 - 121 = 59
Thus meaning the missing exterior angle measure is 59 degrees.
I hope this helped! :)
CAN YOU MARK ME BRAINLIEST PLEASE.
Hey there ...here is ur answer ..
Please mark me as brainliest if u find it helpful ..
Thank u
Write all integers between:
a. -17 and -12
b. -1 and -6
Answers
Answer:
look at explanation
Step-by-step explanation:
a) -13,-14,-15,-16
b) -2,-3,-4,-5
Explain how the unit rate and slope of a proportional relationship are related to each other
Answers
The relationship between unit rate and slope can be found by forming the equation of a straight line.
How to find the proportional relation between two quantities?The two quantities are said to be proportional when the ratio of each of their values are equal.
It can be of two type direct or indirect.
For direct relation the ratio is greater than one for indirect it is less than one.
The example to explain the given case is as follows,
The price and number of pens are proportional to each other.
Suppose the cost of y pens be x.
And, the cost for each pen is m.
Then, the cost for each pen can also be found by the ratio as,
m = y/x
=> y = mx
Which represents a straight line having slope m.
Thus, the unit rate and slope are the equivalent things.
Hence, the unit rate and slope of a proportional relationship are related through the equation of a straight line.
To know more about proportional relation click on,
https://brainly.com/question/3314314
#SPJ2
How do i turn a line graph into a equation
Answers
Answer:
Read lol.
Step-by-step explanation:
Ok for example with the graph below. You want to find the slope. The slope of this graph is 4/5, because I did the technique rise over run. You want to find a point on the line that is in the middle of a square and then find another point and measure. Go up until it meets the other and then go left or right depending on the direction of the line.
After you find the slope you want to find the y-intercept. To find the y-intercept take any point on the line and plug it into this formula with the slope: y=mx+b
So I took the point (0,3): 3=(4/5)(0)+b
Solve: 3=0+b
3=b
And then wen u have all the right material for your equation, you can plug it all in, which gets me: y=4/5x+3
The school that Kathryn goes to is selling tickets to a spring musical. On the first day
of ticket sales the school sold 12 senior citizen tickets and 14 student tickets for a total
of $132. The school took in $108 on the second day by selling 12 senior citizen tickets
and 10 student tickets. What is the price each of one senior citizen ticket and one
student ticket?
Answers
Answer:
Senior citizen ticket = $4, student ticket = $6
Step-by-step explanation:
To do this, form a system of equations where x = the cost for a senior citizen ticket and y = the cost for a student ticket.
Since 12 senior citizen tickets and 14 students tickets cost $132, you get
12x + 14y = 132.
Since 12 senior citizen tickets and 10 students tickets cost $108, you get
12x + 10y = 108.
You can subtract those two equations, so
12x + 14y = 132
-(12x + 10y = 108)
and you get
4y = 24
divide both sides by 4
y = 6
substituting into the equation 12x + 10y = 108,
12x + 10(6) = 108
12x + 60 = 108
subtract 60 from both sides
12x = 48
divide both sides by 12
x = 4
A senior citizen ticket costs $4 and a student ticket costs $6.
help no comprehension
Answers
Answer:
x=17
Step-by-step explanation:
So the outside angle is basically is an addition of the two angles given to you. 60°+2x°=94°.
Graphing a linear inequality in the plane: Standard form
Answers
Answer:
attached
Step-by-step explanation:
draw line pass (-12,0) and (0,3), solution is the shaded part
I WILL GIVE BRAINLIEST!!!
Which of the following correctly uses absolute value to show the distance between −70 and 13? (5 points)
−70 − 13| = |−83| = −83 units
|−70 − 13| = |−83| = 83 units
|−70 + 13| = |−57| = 57 units
|−70 + 13| = |−57| = −57 units
Answers
Answer:
|−70 − 15| = |−85| = 85 units - B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
First of all, distance cannot be negative so you eliminate answers A and D immediately.
Now to find the distance between a negative number and a positive number, you either have to take the absolute value of the negative number (to turn it positive) and add it to the positive or take the absolute value of the positive number subtracted by the negative number.
Basically, you're doing this because it compensates for the distance between the negative number and 0.
The only answer choice that is consistent with these terms is B.
PLSSS HELP ME PLSSS
14 POINTS!
Answers
Answer:
3/4
Step-by-step explanation:
3. For which equation is the ordered
pair (2,8) a solution?
A y=32-3 Cy=3x + 2
B y=x-6 Dy=22 – 14
Answers
Answer:
C
Step-by-step explanation:
y = 3x + 2
Substitute the values
8 = 3(2) + 2
8 = 6 + 2
8 = 8
Equation is true, therefore a solution
A BMX show has
416
people in attendance. If
312
attendees are under the age of
35
,
what is the ratio of attendees under the age of
35
to attendees
35
and older?
Answers
Answer:
The ratio is 3 : 1.
Step-by-step explanation:
Given that:
Number of attendees in the show = 416
Number of people under 35 = 312
Number of people 35 and older = 416 - 312 = 104
Ratio of attendees under 35 to attendees 35 and older
Attendees under 35 : Attendees 35 and older
312 : 104
3 : 1
Hence,
The ratio is 3 : 1.
Briana buys a reel of thread for sewing. Th ere are 10 m of thread on the real. Her brother in grade 4 used 210 cm. How much is left on the reel in centimeters?
Answers
Answer:
790cm
Step-by-step explanation:
Briana buys a reel of thread for sewing. There are 10 m of thread on the real. Her brother in grade 4 used 210 cm. How much is left on the reel in centimeters?
1m = 100cm
10m = x
x = 10 × 100cm
x = 1000cm
The total number of thread on the reel = 1000cm
The amount of thread left on the reel is calculated as:
The total number of thread on the reel - The amount of thread on the reel that was used.
= 1000cm - 210cm
= 790cm
The track coach is putting shoes into bins. if she puts 6 shoes into each of b bins for a total of 54 shoes, how many bins, b, does she have? Solve 6b = 54
For b
Answers
Answer:
9
Step-by-step explanation:
[tex]54 \div 6 = 9[/tex]
[tex]b = 9[/tex]
The coach will have 9 bins
Can ANYONE help write this in slope intercept form??
3х - y = -3
Answers
Answer:
y=3x+3
Step-by-step explanation:
3x-y=-3
-y=-3x-3
y=3x+3
A textbook store sold a combined total of 350 history and physics textbooks in a week. The number of physics textbooks sold was 86 less than
the number of history textbooks sold. How many textbooks of each type were sold?
Answers
Tom ordered some books online and spent a total of $75. Each book cost $6 and he paid a total of $3 for shipping. How many books did he buy? (a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 75, 6, and 3. Let b represent the number of books. (b) Solve the equation in part (a) to find the number of books.
Answers
Answer:
a)
_b+_=_
6B+3=75
B)
He ordered 12 books
Step-by-step explanation:
so each book (b) costs $6. he payed $75 total including the $3 shipping price
That gets us:
6b+3=75
6b=72
b=12
Therefore, Tom ordered 12 books
Determine if the following triangle is a right triangle or not using the Pythagorean Theorem Converse. Triangle with side lengths of: 10 m, 8 m, and 14 m
False, these measures do not form a right triangle.
True, these measures do form a right triangle.
Answers
Answer:
False
Step-by-step explanation:
[tex]{a}^{2} + {b}^{2} = {c}^{2} \\ {10}^{2} + {8}^{2} = {14}^{2} \\ 100 + 64 = 196 \\ 164 < 196[/tex]
These measures do not form a right triangle, but an obtuse triangle.
A 3-gallon container of window cleaner costs $30.72. What is the price per quart?
Answers
Answer: The answer to your question is: 1 quart = $2.56
Step-by-step explanation: data
3-gallon cost = $30.72
cost of 1 quart = 2.56
Rule of three
1 gallon --------------- 4 quarts
3 gallons --------------- x
x = 12 quarts
12 quarts --------------- $30.72
1 quart ---------------- x
x = 1x 30.72 / 12 = $ 2.56
The image of the point (-1, -1)(under a translation is (4, 4)( Find the coordinates of the image of the point (-6, 5) under the same translation.
Answers
to get from (-1,-1) to (4,4) you go right 5 and up 5. Or just adding 5 to both -1s. Doing the same to (-6,5) gives you (-1,10)
The coordinates are (-1, 10).
What is translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions. Since it is just moving of the shape from one place to other, there is no change in the shape.
Translation is one of the transformations in math. When a shape has been transformed, the original shape is called the preimage and the vertices are usually labeled using uppercase letters (Example: ABCD). The translated shape is called the image and the vertices are labeled using uppercase letters with a “prime” next to each (Example: A′B′C′D′, and is pronounced “A-prime, B-prime, C-prime, D-prime”).
Given:
the point is (-8, 3) whose image point is (-5, 2)
The difference between the coordinates of the image and the coordinates of the original is the same for both points.
X - (-6, 5) = (4, 4) -(-1, -1)
X = (4, 4) -(-1, -1) +(-6, 5) = (4+1-6, 4+1+5)
X = (-1, 10)
Hence, the point is (-1, 10)
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ5
Write an expression for the total amount Carla has paid after a certain number of months
Answers
Answer:
$25.00+$36.00m
Step-by-step explanation:
plz help
please do this plz plz plz
Answers
25
7
Therefore,
Base =7 and Hypotenuse =25
Therefore, Perpendicular =
25
2
−7
2
=
625−49
=
576
=24
Hence,
tanA+cotA=
7
24
+
24
7
=
168
576+49
=
168
625
Find the value of 2x + 10 when x = -4
Answers
Answer:
2
Step-by-step explanation:
So basically all you have to do is substitute x = -4 into the equation, so it would be:
[tex]2x + 10 --> 2(-4) +10[/tex]
[tex]=-8 + 10[/tex]
[tex]=2[/tex]
hope that makes sense!
-8 + 10 = 2
The answer is 2
Hope this helps
hii please help i’ll give brainliest if you give a correct answer
Answers
Answer:
x * 3/8(s) = 5/4
5/4 ÷ 3/8(s) = x
Step-by-step explanation:
Answer:
Step-by-step explanation:
How many 3/8 are in 5/4? We can set this number as x. Therre are x number of 3/8 that make up 5/4:
Therefore the PART A is: x* 3/8 = 5/4
On the other hand, 5/4 / 3/8 = x (this is just the reverse of what I mentioned earlier)
I hope this helps! :)
