List the possible rational roots and actual rational roots for the equation x^3+2x^2-5x-6=0

Step-by-step explanation:

A cubic polynomial is given to us . And we need to find the rational roots . Rational roots means the roots which really exits and not imaginary . The given polynomial is :-

On equating it with 0 , it becomes cubic equation. That is ,

Here we will factorise out the given equation and then equate it with 0 to find the roots . Here the constant term is 6 . So the possible factors is 6 is :-

So put them one by one checking out the factors .

Put x = 2 :-

This implies that (x-2) is a factor of p(x) . Now let's divide the polynomial by (x-2) .

x-2 ) x³ + 2x² - 5x -6 ( x² +4x +3

⠀⠀⠀ (-) x³(+) -2x²

_____________

⠀⠀⠀+4x² -5x - 6

⠀⠀⠀ (-) 4x² (+) -8x

_____________

⠀⠀⠀ 3x -6

⠀⠀⠀(+) 3x(+) - 6

_______________

⠀⠀⠀⠀ 0

Hence we can write , x³ +2x² -5x -6 as ,

Equating it with 0 .

answer:

step-by-step explanation: