1. Explain how to determine the equation of the function with the following zeros. Be sure to explain each step as you show how to determine the equation. -5 multiplicity 2 -2 m…

Question

asked Feb 19, 2021 44.0k views

1 Answer

The Paul · Answer 1 · 2021-02-24T03:58:20+0000

Answer:

P(x)=x^3+12x^2+45x+50

Explanation:

Roots of a polynomial

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)

Where a is an arbitrary constant.

We are given the following roots:

-5 multiplicity 2 (-5 twice)

-2 multiplicity 1

Thus, the polynomial is:

P(x)=a(x-(-5))(x-(-5))(x-(-2))

P(x)=a(x+5)(x+5)(x+2)

We are not given any clue about the value of a, so we choose a=1. Multiplying:

P(x)=(x^2+5x+5x+25)(x+2)=(x^2+10x+25)(x+2)

P(x)=x^3+2x^2+10x^2+20x+25x+50

Simplifying:

$\mathbf{P(x)=x^3+12x^2+45x+50}$