Question

Find the rational roots of x4 + 5x3 + 7x2 – 3x – 10 = 0.

Answer 1

Given:

The function is,

$x^4+5x^3+7x^2-3x-10=0$

Use the synthetic division,

The rational roots are of the form,

$\frac{p}{q}$

As, the constant term is -10, its factors are

$\pm1,\pm2,\pm5,\pm10$

These are the possible values of p.

Also, the leading coefficient is 1. its factors are

$\pm1$

These are the values of q.

From the above synthetic division, the actual rational roots are,

$1,-2$

Answer: rational roots are -2, 1