SOLUTION: Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the given conditions. zero of 2 and zero of 4 having multiplicity 2; f(1)=-18

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Question 1029945: Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the given conditions.

zero of 2 and zero of 4 having multiplicity 2; f(1)=-18
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+k%28x-2%29%28x-4%29%5E2 for some undetermined constant k.
Now f%281%29+=+k%281-2%29%281-4%29%5E2+=+-18 ==> -9k = -18 ==> k = 2.
f%28x%29+=+2%28x-2%29%28x-4%29%5E2 is the polynomial function of degree 3. (Just do the necessary expansion.)