For the following exercises, use the given information about the polynomial graph to write the equation. Roots of multiplicity 2 at x = −3 and x = 2

Aneeka Hunt

Aneeka Hunt

Answered question

2021-09-24

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x=−2. y-intercept at (0, 4).

Answer & Explanation

liingliing8

liingliing8

Skilled2021-09-25Added 95 answers

Data: x — intercept of multiplicity 2= —3,2
© — intercept of multiplicity 1=-2
y—intercept = 4
Degree=5
Since it is a fifth degree polynomial function with multiplicity of 2 and 1 for some zeros, its general equation becomes: f(x)=a(x+3)2(x2)2(x+2)
In order to evaluate a, use the point on the graph (0,4), therefore substitute f(0) =4 in this equation:
4=a(0+3)2(02)2(0+2)
Simplify: 4=a(3)2(2)2(2)=72a
Evaluate a: a=472=118
This implies that the equation of the given polynomial function is f(x) =
118(x+3)2(x2)2(x+2)

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