SOLUTION: Find a polynomial f(x)of degree 3 with real coefficients and the following zeros. 4,2+i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial f(x)of degree 3 with real coefficients and the following zeros. 4,2+i      Log On


   

Question 681921: Find a polynomial f(x)of degree 3 with real coefficients and the following zeros.
4,2+i
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
given zeros
4 and 2+i
...
unstated but known
2-i as it is the conjugate pair
...
x=4, so x-4=0
x=2+/-i, so x-2= +/- i; therefore sqrt%28x-2%29%5E2+=+sqrt%28-1%29 and %28x-2%29%5E2=-1, which is %28x-2%29%5E2%2B1=0
...
Taking (x-4) and %28x-2%29%5E2%2B1, which is x%5E2-4x%2B2%2B1
and multiplying them
(x-4)(x%5E2-4x%2B3)
to get
x%5E3+-+4x%5E2+%2B+3x+-+4x%5E2+%2B+16x+-+12
combine like terms
highlight_green%28x%5E3+-+8x%5E2+%2B+19x+-+12%29
.....................
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