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

BenoguigoliB 2021-09-24 Answered
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 = −2. y-intercept at (0, −3).
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escumantsu
Answered 2021-09-25 Author has 98 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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