Solve by finding all roots; x^4-3x^3-x^2-27x-90=0?

Answer 1

x = -2, x=5, x =3i, x= -3i
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here is the factoring:

= (x^4 - x^2 -90) -(3x^3 + 27x)

=(x^2 - 10)(x^2 + 9) - 3x(x^2 + 9)

=(x^2 +9)(x^2 -3x -10)

=(x^2 + 9)(x+2)(x-5)

Two real and two complex roots.

Answer 2

x^4 - 3x^3 - x^2 - 27x - 90 = 0
x^4 - 3x^3 - x^2 - 27x = 90
x (x^3 - 3x^2 - x - 27) = 90
x = 90

x^3 - 3x^2 - x - 27 = 90
x^3 - 3x^2 - x = 117
x (x^2 - 3x - 1) = 117
x = 117

x^2 - 3x - 1 = 117
x^2 - 3x - 118 = 0
quadratic formula..

3 +/- (sqrt. 3^2 - 4(1)(-118)) over 2
3 +/- (sqrt. 481) over 2
x= 12.466
x= -19.932

So in all, x = 90, 117, 12.466, -19.932
Wow, that was pretty challenging.