Question

How do you find the real solutions of the polynomial `x^3+6=2x^2+5x`?

Answer 1

Solution: `x=1 ,x=3 ,x=-2`

Explanation:

`x^3+6=2x^2+5x or x^3+6-2x^2-5x =0` or

`x^3-2x^2-5x +6 =0 or x^3-x^2-x^2+x-6x+6 =0` or

`x^2(x-1)-x(x-1)-6(x-1) =0` or

`(x-1)(x^2-x-6)=0 or (x-1) ( x^2-3x+2x-6)=0` or

`(x-1) { x(x-3)+2(x-3)}=0` or

`(x-1) {(x-3)(x+2)}=0` or

`(x-1)(x-3)(x+2)=0`

`x-1=0 :. x=1 or x-3=0 :.x=3` or

`x+2=0:. x =-2`

Solution: `x=1 ,x=3 ,x=-2` [Ans]