# How do you use the rational root theorem to find the roots of 314x^3+1099x^2-1413?

The roots are $1 , - 3 , - \frac{3}{2}$

#### Explanation:

You can use the rational root theorem as follows

1)Find all the factors of the constant term.In our case is -1413
2)Among these factors there are possible roots of the polynomial

Hence we have that the divisors of 1413 are

$1 , 3 , 9 , 157 , 471 , 1413$

Hence by error and trial we find the roots and write the polynomial as

$314 {x}^{3} + 1099 {x}^{2} - 1413 = 157 \left(x - 1\right) \left(x + 3\right) \left(2 x + 3\right)$