Question

Find rational roots of the polynomial f(x) = 2x³ + x² − 7x − 6.

Answer 1

The given polynomial is

f(x) is a cubic polynomial with integer coefficients. If $\frac{b}{c}$ is rational root in lowest terms, then the values of b are limited
to the factors of 6 which are $\pm 1,\pm 2,\pm 3,\pm 6$ and the values of c are limited to the factor of 2 as $\pm 1,\pm 2$. Hence, the possible
rational roots are $\pm 1,\pm 2,\pm 3,\pm 6,\pm \frac{1}{2},\pm \frac{3}{2}$.

Since,

So, 2 is a root of the polynomial

Now, the polynomial can be written as,

Also,

Therefore,

Hence, the rational roots of the polynomialare 2, – 3/2 and – 1.