SOLUTION: Can you help me find a third degree polynomial with a polynomial function with real coefficients that has -3 and i as zeros and such that f(1) =8?

Question 1095516: Can you help me find a third degree polynomial with a polynomial function with real coefficients that has -3 and i as zeros and such that f(1) =8?
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Can you help me find a third degree polynomial with a polynomial function with real coefficients that has -3 and i as zeros and such that f(1) =8?
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You do Step 1:
f(x) = (x+3)*(x-i)*(x+i)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If the polynomial has real coefficients, then complex or imaginary roots must occur in conjugate pairs. So if i is a root, -i is another root.

That makes the three roots -3, i, and -1; the polynomial is of the form

where a is a constant.

The value of the constant a is determined using the given information that f(1) is 8. So to find the value of a and thus finish finding the exact polynomial, solve the equation f(1) = 8:

I'll let you finish from there....
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