已知多项式f(x)=2x^4-x^3-8x^2+x+6有三个整数根,则第四个根是?

f(x)=2x^4-x^3-8x^2+x+6
=2x^4 - 2x^3 + x^3 - x^2 - 7x^2 + 7x - 6x + 6
=2x^3(x-1) + x^2(x-1) - 7x(x-1) - 6(x-1)
=(x-1)(2x^3 + x^2 - 7x - 6)
=(x-1)(2x^3 + 2x^2 - x^2 - x - 6x - 6)
=(x-1){2x^2(x+1) - x(x+1) - 6(x+1)}
=(x-1)(x+1)(2x^2 - x - 6)
=(x-1)(x+1)(x-2)(2x+3)
三个整数根,分别是 1 ,-1 ,2
第四个根是,-3/2