Find polynomial function P of the lowest possible degree, having real coefficients , a leading coefficient of 1 and with given zeros 2+3i, -1, and 2
start by writing each root as x =.
x = 2 + 3i
x = -1
x = 2
Then set them equal to zero.
x = 2 + 3i is the hard one.
subtract 2 from each side: x - 2 = 3i
square each side: x^2 - 4x + 4 = -9
add 9: x^2 - 4x - 13 = 0
x= -1 add 1 to each side so, x + 1 = 0
x = 2 subtract 2 from each side so, x - 2 = 0
Now multiply all together,
(x^2 - 4x + 4)(x + 1) (x -2)
x^4 -5x^3+8x^2+2x-8
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