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 1029942: 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 josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Zeros are 2 and 4 and 4 again.

f%28x%29=k%28x-2%29%28x-4%29%5E2, which takes care of the zeros.
f%28x%29=k%28x-2%29%28x%5E2-8x%2B16%29
k%28x%5E3-8x%5E2%2B16x-2x%5E2%2B16x-32%29
highlight%28k%28x%5E3-10x%5E2%2B32x-32%29%29, and then seems your choice to multiply through by k or not.

Finding k should be easier using the fully factored form.
f%281%29=k%281-2%29%281-4%29%5E2=-18
k%28-1%29%28-3%29%5E2=-18
k%28-1%29%2A9=-18
k=2

Now you can multiply through using k=2.
highlight%28highlight%28f%28x%29=2x%5E3-20x%5E2%2B64x-64%29%29