Question 697552: what is the equation that has zeros at 4 and 2+5i
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! what is the equation that has zeros at 4 and 2+5i
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Based on the zeros, factors must be:
(x-4)(x+2+5i)(x+2-5i)
just multiply the above together to get your equation:
(x-4)(x(x+2-5i)+2(x+2-5i)+5i(x+2-5i))
(x-4)(x^2+2x-5xi+2x+4-10i+5xi+10i-25)
(x-4)(x^2+4x-5xi+4-10i+5xi+10i-25)
(x-4)(x^2+4x+4-10i+10i-25)
(x-4)(x^2+4x+4-25)
(x-4)(x^2+4x-21)
x^2(x-4)+4x(x-4)-21(x-4)
x^3-4x^2+4x^2-16x-21x+84
x^3-16x-21x+84
x^3-37x+84
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