Web Analytics
Answered

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


2x³+5x²-8x-10=0

A{±2/5, ±1/2, ±1, ±2, ±2/5, ±1/5, ±1/10}
B{±1/2, ±1, ±2, ±5/2, ±5, ±10}
C{±1, ±2, ±4, ±5, ±10, ±20}
D{1/2, 1, 2, 5/2, 4, 5, 10, 20} ...?

Verified Answer :

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.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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

Related Questions