According to the rational root theorem, which is not a possible rational root of 5x3 + 3x2 – 2x + 15 = 0?

Question

According to the rational root theorem, which is not a possible rational root of 5x³ + 3x² – 2x + 15 = 0?

A. 1/3

B. 1/5

C. 5

D. -3

 

Answer 1

If p/q is a rational root of the given polynomial, then p is a divisor of the constant term, 15, and q is a divisor of the leading coefficient, 5.

 

So, p = ±(1, 3, 5, 15) and q = ±(1, 5).  Therefore, the only possible rational roots are ±(1, 1/5, 3, 3/5, 5, 15).  Thus, 1/3 is not possible as a rational root for the given polynomial.  

 

ANSWER: A