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Answer:
Step-by-step explanation:
We are given that function <em>f</em> is a polynomial of degree 3. It has a root of multiplicity 2 at <em>u</em> = 4, f(-4) = 0, and f(0) = -28.8. We want to determine an algebraic equation for <em>f</em>.
First, since it has a root of multiplicity 2 at <em>u</em> = 4, one factor is:
Furthermore, since f(-4) = 0, <em>f</em> has another root at <em>u</em> = -4. Since the degree of <em>f</em> is 3, the multiplicity of this root must be 1. Hence, the other factor is:
Hence, our function is:
Since f(0) = -28.8, <em>f</em> = -28.8 when <em>u</em> = 0. Find <em>a: </em>
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In conclusion, our function will be: