 # 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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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: $f\left(x\right)=a\left(x+2\right){\left(x—1\right)}^{2}{\left(x-4\right)}^{2}$
In order to evaluate a, use the point on the graph (0,-3), therefore substitute f(0)=-3 in this equation:
$-3=a\left(0+2\right)\left(0—1\right){\left(0-4\right)}^{2}$
Simplify: -3=-32a
Evaluate a: $a=-\frac{3}{-32}=\frac{3}{32}$
This implies that the equation of the given polynomial function is f(x) =
$\frac{3}{32}\left(x+2\right)\left(x—1\right){\left(x-4\right)}^{2}$