SOLUTION: Math Question: Find a polynomial function f(x) of degree 3 with real coefficients that has zeros of -1,2,and 4 and f(1)=3.

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Question 838075: Math Question: Find a polynomial function f(x) of degree 3 with real coefficients that has zeros of -1,2,and 4 and f(1)=3.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=a%28x%2B1%29%28x-2%29%28x-4%29}
That satisfies the three zeros.
Now use the value to solve for a.
f%281%29=a%281%2B1%29%281-2%29%281-4%29=3
a%282%29%28-1%29%28-3%29=3
6a=3
a=1%2F2
highlight_green%28f%28x%29=%281%2F2%29%28x%2B1%29%28x-2%29%28x-4%29%29