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 = 1

Suman Cole

Suman Cole

Answered question

2021-09-28

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 = 1, and a root of multiplicity 1 at x = −3. y-intercept at (0, 9)

Answer & Explanation

SchepperJ

SchepperJ

Skilled2021-09-29Added 96 answers

Data: x — intercept of multiplicity 2=1.3
© — intercept of multiplicity 1=-3
y—intercept = 9
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)(x1)2(x3)2
In order to evaluate a, use the y - intercept (0,9), therefore substitute f(0)=9 in this equation:
9=a(0+3)(01)2(03)2
Simplify: 9=27a
Evaluate a: a=927=13
This implies that the equation of the given polynomial function is f(x) =
13(x+3)(x1)2(x3)2

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