Question 186246
how do i find the 4th degree polynomial with real coefficients that has zeros of -2, 3, 1+4i, and 1-4i?
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Deal with (1 +/- 4i) fir4st
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x = 1 +/- 4i
x - 1 = +/-4i
Square both sides:
(x-1)^2 = (4i)^2
x^2 - 2x + 1 = 16i^2
x^2 - 2x + 1 = 16(-1)
x^2 - 2x + 1 = -16
x^2 - 2x + 1 + 16 = 0
x^2 - 2x + 17
:
x = -2:
(x^2 - 2x + 17) * (x+2) = x^3 + 13x + 34
:
x = 3
(x^3 + 13x + 34) * (x-3) = (x^4 - 3x^3 + 13x^2 - 5x - 102) is the 4th degree polynomial