solve : 2x^4 -11x^3 + 12x^2 + x - 4 = 0

Answer 1

4 possible solutions

try some simple integers such as x=1

2x^4 -11x^3 + 12x^2 +x -4

2 -11 +12 +1 - 4 = 0

x=1, a factor is x-1. Divide the quadratic by x-1 to get

2x^3 -9x^2 +3x +4

try x=1 again, another factor repeats, x-1

divide x-1 into the cubic

to get

2x^2 -7x -4

(2x+1)(x-4) = 0

x=-1/2, 4

4 real solutions although 1 solution repeats

(x-1)^2(2x+1)(x-4) = 0

(x-1)(x-1)(2x+1)(x-4) = 0

set each factor equal to zero

x=1, 1, -1/2, 4