SOLUTION: Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 3, and zeros 1 and 4 + 4i.

Question 263696: Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions.
P has degree 3, and zeros 1 and 4 + 4i.
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Given zeros are 1 and 4+4i
We know that complex roots occur in conjugate pairs.
Since 4+4i is one zero, 4-4i is also another zero.
The required equation is
(x-1)[x-(4+4i][x-(4-4i)] = 0
(x-1)[(x-4)-4i][(x-4)+4i] = 0
(x-1)[(x-4)^2-(4i)^2]=0
(x-1)[x^2-8x+16+16] =0
(x-1){x^2-8x+32]=0
x^3-8x^2+32x-x^2+8x-32=0
x^3-9x^2+40x-32 = 0
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