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Find a polynomial function P of the lowest possible degree having real coefficie

Mathematics
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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

Mar 1st, 2015

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

Mar 1st, 2015

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