solve : x^4 + 2x^3-7x^2-8x+12=0

Answer 1

x^4 +2x^3 -7x^2 -8x + 12 = 0

try x=1, it works

1+2-7-8+12 = 0

x-1 is a factor, divide it into the quadratic to get

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

try x=2, it also works

2^3 +3(2^2) - 4(2) -12 = 8+12-8-12 = 0

x-2 is another factor

divide x-2 into the cubic polynomial

leaving a quadratic, x^2 +5x +6

which factors into

(x+3)(x+2) = 0

x =-2, -3

4 real solutions

x =-2, -3, 1, 2