complex numbers?

Question

The question is with the given equation solve for all values of x over the complex numbers
the equation is 2x^4 +x^3 -20x^2+29x-12=0
help what do i do thanks

Answer 1

According to the rational root theorem, if a/b is any zero
of p = 2x^4 +x^3 -20x^2+29x-12 then a must divide
12 and b must divide 2.
Testing some divisors of 12, we see that 1 is a zero of p,
so x-1 is a factor of p.
The quotient, q, obtained by long division or synthetic
division is:
2x³ +3x² -17x + 12.
Again, 1 is a zero of q, so x-1 is a factor of q.
The quotient is
2x² + 5x -12.
Setting this equal to zero and solving yields
(x+4)(2x-3) = 0
So x = -4 and x = 3/2.
Thus p has 1 (a double root), -4 and 3/2 as zeros.