You can put this solution on YOUR website! can anyone help me with this question: find a polynomial with integer coefficients that has the given zeros 3, 3+i
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First factor is easy:
x = 3
1st factor is: (x-3)= 0
:
x = 3 + i
Think of it as the reverse of completing the square
x - 3 = i
Square both sides
(x-3)^2 = i^2;
x^2 - 6x + 9 = -1: FOILed (x-3(x-3); we know that i^2 = -1
x^2 - 6x + 9 + 1 = 0
x^2 - 6x + 10 = 0; is the 2nd factor
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Multiply the two factors the long way:
(x-3) * (x^2 - 6x + 10) = x^3 - 9x^2 + 28x - 30 is the polynomial
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