SOLUTION: how do you find he remaining zeroes of f if the degree of a polynomial is 4, and the zeroes are i,2 and-2

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Question 1125241: how do you find he remaining zeroes of f if the degree of a polynomial is 4, and the zeroes are i,2 and-2
Found 3 solutions by MathLover1, solver91311, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
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if the degree of a polynomial is 4, there is four zeros
and, if the zeroes are x%5B1%5D=i,x%5B2%5D=2 and x%5B3%5D=-2, missing fourth zero is x%5B4%5D=-i because complex zeros always come in pairs
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x-i%29%28x-2%29%28x-%28-2%29%29%28x-%28-i%29%29
f%28x%29=%28x-i%29%28x-2%29%28x%2B2%29%28x%2Bi%29
f%28x%29=%28x-i%29%28x%2Bi%29%28x-2%29%28x%2B2%29
f%28x%29=%28x%5E2-i%5E2%29%28x%5E2+-+4%29
f%28x%29=%28x%5E2-%28-1%29%29%28x%5E2+-+4%29
f%28x%29=%28x%5E2%2B1%29%28x%5E2+-+4%29
f%28x%29=x%5E4%2Bx%5E2+-+4x%5E2-4
f%28x%29=x%5E4-+3x%5E2-4




Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Since f is of degree 4, there are exactly 4 zeros, counting multiplicities. Complex zeros ALWAYS appear in conjugate pairs, i.e. if is a zero, then must also be a zero.

Since is a zero, then must also be a zero.


John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your condition is FATALLY incomplete, missing the statement that the polynomial has real coefficients.


Only in this case and only under this assumption the conjugate complex roots go in pairs.