For the following exercises, use the given information about the polynomial graph to write the equation. Degree 4. Root of multiplicity 2 at x = 4, an

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Answered question

2021-06-20

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 4. Root of multiplicity 2 at x=4, and roots of multiplicity 1 at x=1 and x=minus;2. y-intercept at (0, minus;3).

Answer & Explanation

Alix Ortiz

Alix Ortiz

Skilled2021-06-21Added 109 answers

Data: x - intercept of multiplicity 2=4
intercept of multiplicity 1=2,1
y-intercept =3
Degree=4
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+2)(x1)2(x4)2
In order to evaluate a, use the point on the graph (0,-3), therefore substitute f(0)=3 in this equation:
3=a(0+2)(01)(04)2
Simplify: -3=32a
Evaluate a: a=332=332
This implies that the equation of the given polynomial function is f(x)=
332(x+2)(x1)(x4)2

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