Question

How do you use the rational root theorem to find the roots of `x^3 + 2x^2 + 3x + 6 = 0`?

Answer 1

-2, `+-isqrt3`

Explanation:

The degree of the polynomial on then left side is odd and the coefficient of its leading term is 1, hence the product of the roots would be -6, these can be `+-1, +-2, +-3, +-6`.

Out of these values x= -2 makes the polynomial on the left side 0, hence x+2 would be factor of the polynomial. Now divide the polynomial by x+2,

From this factorisation, the roots can be writtne as -2, `+-isqrt3`