Question

For the function `g(x)=x^3+x^2-6x`, how do you find at least one value of x for which g(x)=0?

Answer 1

`{x : g(x)=0}={-3,0,2}.`

Explanation:

`g(x)=0 rArr x^3+x^2-6x=0.`

`rArr x(x^2+x-6)=0.`

`rArr x{ul(x^2+3x)-ul(2x-6)}=0.........[3xx2=6, 3-2=1].`

`rArr x{x(x+3)-2(x+3)}=0.`

`rArr x(x+3)(x-2)=0.`

Hence, the Desired Set`={x : g(x)=0}={-3,0,2}.`