Question

According to the rational root theorem, which of the following are possible

Answer 1

Given:

The polynomial function is

$F(x)=4x^3-6x^2+9x+10$

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of $\dfrac{p}{q}$, where, p is a factor of constant and q is the factor of leading coefficient.

We have,

$F(x)=4x^3-6x^2+9x+10$

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

$x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}$

Therefore, the correct options are A, C, D, F.