Question

Which values are possible rational roots of 4x3+9x2−x+10=0 according to the rational root theorem? Select each correct answer. ±12 ±2 ±52 ±25

Answer 1

ANSWER

The possible rational roots are:

$\pm\frac{1}{2},\pm2,\pm \frac{5}{2}$

EXPLANATION

According to the rational root theorem, the possible rational roots of the polynomial,

$4x^3+9x^2-x+10=0$

are all the possible factors of the constant term divided by all the possible factors of the coefficient of the highest degree of the polynomial.

Therefore we examine the numerator and denominator of the options provided to see if they are factors of 10 and 4 respectively.

For

$\pm\frac{1}{2}$, we can see that 1 is a factor of 10 and 2 is a factor of 4, hence it is a possible rational root.

The same thing applies to $\pm2,\pm \frac{5}{2}$ also.

As for

$\pm \frac{2}{5}$, 2 is a factor of 10 but 5 is not a factor of 2, hence it is not a possible rational root.