Question

Find all rational roots for p(x)=0

P(x)=6x^4-13x^3+13x^2-39x-15

A. No rational roots
B. 1/2,1/3
C. 5/2,1/3
D. -1/2,5

Answer 1

C. (5/2, -1/3)

Step by step explanation

Here we use the rational root theorem.

The possible roots are

+1, +3, +5, +15, +1/2, +3/2, +5/2, +15/2, +1/3, +5/3, +1/6 and +5/6

We have to use the synthetic division to find the correct root of this function.

Here the roots are 5/2 and -1/3

Others are not roots of this function.

Let's check x = 5/2 with synthetic division.

5/2) 6 -13 13 -39 -15

- 15 5 45 15

--------------------------

6 2 18 6 0

Similarly x = -1/3 is also root of this function.

Answer: C. (5/2, -1/3)