Cubic Equations
posted by Belinda on .
I have three that I need help with if possible.
1. Solve 2x^3  3x^2 = 6x  9
2. Find all real and imaginary roots of the polynomial equation 3x^4  x^3 + 4x^2  2x  4=0
3. Find a cubic equation with integral coefficients and roots 3i and 5.

2 x^3 3 x^2 6 x + 9 = 0
(2x^3  6x)  (3 x^29) = 0
2x (x^23) 3(x^23) = 0
(x^23)(2x3) = 0
you take it from there.
2)
Try x = 1
31+424 = 0 amazing
so divide by (x1)
(x1)(3x^3+2x^2+6x+4) = 0
(x1)[ 3x(x^2+2) + 2(x^2+2) ]
you take it from there
3)
(x+5)(x3i)(x+3i)
if you have 3i, then you must have the complex conjugate 3i 
Thanks so much :D