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Which of the following describes the roots of the polynomial function f(x)=(x-3)*(x+6)²?-3 with multiplicity 2 and 6 with multiplicity 4
-3 with multiplicity 4 and 6 with multiplicity 2
O3 with multiplicity 2 and-6 with multiplicity 4
O3 with multiplicity 4 and -6 with multiplicity 2

Answers

Answer 1
Answer:

Final answer:

The roots of the polynomial function f(x)=(x-3)*(x+6)² are 3 and -6.


Explanation:

The polynomial function f(x)=(x-3)*(x+6)² can be factorized as follows:

f(x) = (x-3)*(x+6)*(x+6)

This means that the expression (x-3) represents one of the linear factors of the polynomial, while (x+6) represents a quadratic factor. To find the roots of the polynomial, we set each factor equal to zero and solve for x:

(x-3) = 0 -> x = 3

(x+6) = 0 -> x = -6

Therefore, the roots of the polynomial function f(x)=(x-3)*(x+6)² are 3 and -6.


Learn more about Polynomial roots here:

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Related Questions

A jar contained 8 balls: 6 red, 1 green and 1 blue. We randomly take a ball out of the jar. Once a ball is selected we do not put it back. We keep selecting balls until for the first time we get a blue one. We count the number of times we had to draw a ball, (including the last drawing) until we actually got the blue ball. How many elements are in the sample space for this experiment
Which of the following statements is false regarding randomization?
2. Use the graph of y=-x2 - 2x + 3 to solvethe equation –X2 - 2x + 3-0. What arethe solutions?A 4B -1 and 4C 1 and -3
What is the solution to 7.5d=2.5d
Perform the following calculation: (+10) + (–45). A. 55 B. –55 C. –35 D. 35

P(q ÷ 3 - p ); use p = -6, and q= -3

Answers

Answer:

Step-by-step explanation:

p(q ÷ 3 - p )

p = -6

q= -3

-6(-3/3 - (-6))

-6(-1 + 6)

-6(+5)

-30

Lauren is building a tree house with her dad. the dimensions of the floor are 9 feet by 6 feet. what is the area of the floor, measured in the square yards?A. 6 square yards
B. 15 square yards
C. 30 square yards
D. 54 square yards

Answers

Answer:

The answer is A) 6 square yards.
Hello There!

Area = L x W
Area = 9 x 6
Area = 54
Therefore, making your answer D. 54 square yards.

Hope This Helps You!
Good Luck :)

How many strings of length 5 can be written using the letters {a,b,c,d,e,f} if no two consecutive letters can be the same? For example, we'd count adede but not acdde.

Answers

Answer:

3750 strings.

Step-by-step explanation:

First we have 6 different letters to choose from (a, b, c, d, e, f) and we will make a string of length 5.

First, we would have to choose one of the letters, to do this we would have 6 choices.

For our second choice, we can only choose from 5 letters since we cannot choose the one that we already chose (no two consecutive letters can be the same).

Then, for our third choice, we would have to choose from 5 different letters (any letter but the one before).

Similarly for our fourth and fifth choice, we can choose 5 different letters.

Then, the total amount of strings would be:

6 x 5 x 5 x 5 x 5 = 6 x 5⁴ = 3750 strings.

How do you show 239+132 integer form to polynomial form

Answers

Answer:

The answer is "371"

Step-by-step explanation:

First polynomial value = 239

Second polynomial value = 132

Adding the value: = 239+ 132

                               = \boxed{\bold{371}}

The final answer is 371, which is also known as monomial.

Write the rate as a unit rate:
400 miles in 8 hours

Answers

The rate as a unit rate of 400 miles in 8 hours is 50 miles.

What is difference between rate and unit rate ?

"The process of breaking down the cost to a smaller unit reveals the unit rate of the product. Since rate is a ratio that compares two different units."

Based on the given conditions,

Rate as a unit rate :

= (400)/(8)

Cross out the common factor

= 50 miles

Hence, the rate as a unit rate of 400 miles in 8 hours is 50 miles.

Learn more about rate and unit rate here

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#SPJ2

Answer:

50miles/hour

Step-by-step explanation:

400/8 is 50.

An attacker at the base of a castle wall 4 m high throws a rock straight up with speed 7.5 m/s from a height of 1.5 mabove the ground.
(a) Will the rock exceed the top of the wall?
(b) If so, what is its speed when it reaches the top of the wall?
Page 4 of 7
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(c) If we don’t want the stone to exceed the top of the wall (we want the top of the wall to be the maximum height)
what the initial speed that the stone must have?

Answers

Answer:

a) Yes, b)v\approx 2.686\,(m)/(s), c)v_(o) \approx 7.002\,(m)/(s)

Step-by-step explanation:

a) The maximum height reached by the rock is:

\Delta y = (\left(0\,(m)/(s) \right)^(2)-\left(7.5\,(m)/(s) \right)^(2))/(2\cdot \left(-9.807\,(m)/(s^(2)) \right))

\Delta y = 2.868\,m

y = 1.5\,m + 2.868\,m

y = 4.368\,m

Yes, the rock will exceed the top of the wall.

b) The speed when the rock reaches the top of the wall:

v = \sqrt{\left(7.5\,(m)/(s) \right)^(2)+2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m)}

v\approx 2.686\,(m)/(s)

c) The initial speed required so that stone does not exceed the top of the wall is:

v_(o) = \sqrt{\left(0\,(m)/(s) \right)^(2)-2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m) }

v_(o) \approx 7.002\,(m)/(s)
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