SOLUTION: Find the nth-degree polynomial function with real coefficients satisfying the given conditions.
n=4; i and 5i are zeros; f(-1)=52
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Question 763112: Find the nth-degree polynomial function with real coefficients satisfying the given conditions.
n=4; i and 5i are zeros; f(-1)=52
Found 2 solutions by MathLover1, tommyt3rd:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
You are given three roots:
and
since is a root, so must its conjugate also be a root,
since is a root, so must its conjugate also be a root
You can find by using zero product rule
....your polynomial
check if
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
Since coefficients are real this must mean that the complex roots occur in conjugate pairs. We can write:
and given that f(-1)=52 we can determine a...
so that
and a=1
this leads to
:)
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