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

Question

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).

Answer 1

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) {(x — 1)}^{2} {(x - 4)}^{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) (0 — 1) {(0 - 4)}^{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} (x + 2) (x — 1) {(x - 4)}^{2}

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

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