Question

Which of the following represents the set of possible rational roots for the polynomial shown below?

Answer 1

The rational roots are involved by dividing the factors of the constant term by the factors of the coefficient of the monomial of highest degree. Thus, the only possible set of rational roots is given by B.


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Answer 2

Answer:

Option b is correct

Step-by-step explanation:

Given the polynomial

$2x^3+5x^2-8x-10=0$

we have to find the set of possible rational roots for the polynomial.

Rational root theorem states that if P(x)  has any rational roots then they must be of form

$\pm{\frac{\text{Factor of }a_0}{\text{factors of }a_n}$

Here $P(x)=2x^3+5x^2-8x-10$

Factors of 10=1, 2, 5, 10

Factors of 2=1, 2

Possible rational roots are

$\{\pm1, \pm\frac{1}{2}, \pm2, \pm\frac{5}{1}, \pm\frac{5}{2}, \pm 10\}$

Option b is correct