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

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Answer 1 · 2015-09-10T23:43:28

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

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

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

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

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

How do you use the rational root theorem to find the roots of 314x^3+1099x^2-1413314x3+1099x2−1413314x^3+1099x^2-1413?