SOLUTION: find a 4th degree polynomial with real coefficients satisfying the given conditions: -1,5, and 2+4i are zeros; f(1)=-272
Algebra.Com
Question 1169061: find a 4th degree polynomial with real coefficients satisfying the given conditions: -1,5, and 2+4i are zeros; f(1)=-272
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Complex zeros always appear in conjugate pairs, so if 
is a zero, then 
must also be a zero.
Your desired function then has 5 factors, one of which is a constant, thus:
\ =\ a(x\,+\,1)(x\,-\,5)\(x\,-\,(2\,+\,4i)\)\(x\,-\,(2\,-\,4i)\))
You can expand and collect like terms for yourself. Hint: Remember that the product of two conjugates is the difference of two squares and that 
.
Substitute 1 for 
, then do the arithmetic to solve for 
giving you everything you need for your function.
John
My calculator said it, I believe it, that settles it
From
I > Ø
RELATED QUESTIONS
Find an nth degree polynomial function with real coefficients satisfying the given... (answered by josgarithmetic)
Find an nth-degree polynomial function with real coefficients satisfying the given... (answered by Fombitz)
Find an nth-degree polynomial function with real coefficients satisfying the given (answered by Fombitz)
Find an nth degree polynomial function with real coefficients, a leading coefficient of 1 (answered by greenestamps,ikleyn)
Find the nth degree polynomial function with real coefficients satisfying the given... (answered by Fombitz)
find an nth degree polynomial function with real coefficients satisfying the given... (answered by drk)
Find an nth-degree polynomial function with real coefficients satisfying the given... (answered by josgarithmetic)
Find an nth degree polynomial function with real coefficients satisfying the given... (answered by Fombitz)
Find an nth-degree polynomial function with real coefficients satisfying the given (answered by MathLover1)