Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = – 3. The y-intercer

is y = - 13.5.
Find a formula for P(x).

Answer 1

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Answer:

P(x) = -1/2(x -3)²(x +3)

Explanation:

When q is a root of the polynomial, (x-q) is a factor. This polynomial will be ...

P(x) = a(x -3)²(x +3)

For x=0, the y-intercept will be ...

P(0) = 27a = -13.5

Then the value of a is ...

a = -13.5/27 = -1/2

The formula for P(x) is ...

P(x) = -1/2(x -3)²(x +3) . . . . . . factored form

P(x) = -0.5x³ +1.5x² +4.5x -13.5 . . . . standard form