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Stolb23 [73]
3 years ago
5

Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -2 (multiplicity 3), 3 (m

ultiplicity 1), and with f(0) = 120.​
Mathematics
2 answers:
Genrish500 [490]3 years ago
6 0

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -2 (multiplicity 3), 3 (multiplicity 1), and with f(0) = 120.

The first part zeros of -2 means (x+2) and multiplicity 3 means (x+2)^3.

The second part zeros of 3 means (x-3) and multiplicity 1 means (x-3).

The third part f(0) = 120 means substituting x=0 into (x+2)^3*(x-3)*k =120

(0+2)^3*(0-3)*k = 120

-24k = 120

k = -5

Combining all three conditions, f(x)

= -5(x+2)^3*(x-3)

= -5(x^3 + 3*2*x^2 + 3*2*2*x + 2^3)(x-3)

= -5(x^4 + 6x^3 + 12x^2 + 8x - 3x^3 - 18x^2 - 36x - 24)

= -5(x^4 + 3x^3 - 6x^2 - 28x -24)

= -5x^4 - 15x^3 + 30x^2 + 140x + 120

oee [108]3 years ago
4 0

Answer:

Step-by-step explanation:

-2 is a root for 3 times and 3 is root for once

so (x+2)^3 * (x-3) is part of f(x)

the constant term there is 2^3*(-3)=-24

so there is a multiplier of 120/-24=-5

f(x) = 5 * (x+2)^3 * (x-3)

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What are the roots of the equation 2x2<br> 13x + 25 = 0 in simplest a + bi form?
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3 years ago
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6 0
3 years ago
Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following
uranmaximum [27]

Answer:

b. S = 405, D = 0

Step-by-step explanation:

We have been given that profit for a particular product is calculated using the linear equation: \text{Profit}=20S+3D. We are asked to choose the combinations of S and D that would yield a maximum profit.

To solve our given problem, we will substitute given values of S and D in the profit function one by one.

a. S = 0, D = 0

\text{Profit}=20S+3D

\text{Profit}=20(0)+3(0)

\text{Profit}=0

b. S = 405, D = 0

\text{Profit}=20S+3D

\text{Profit}=20(405)+3(0)

\text{Profit}=8100+0

\text{Profit}=8100

c. S = 0, D = 299

\text{Profit}=20S+3D

\text{Profit}=20(0)+3(299)

\text{Profit}=0+897

\text{Profit}=897

d. S = 182, D = 145

\text{Profit}=20S+3D

\text{Profit}=20(182)+3(145)

\text{Profit}=3640+435

\text{Profit}=4075

Since the combination S = 405, D = 0 gives the maximum profit ($8100), therefore, option 'b' is the correct choice.

7 0
3 years ago
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