Question

How many possible rational roots are there for 2x4+4x3−6x2+15x−12=0?

A. 4

B. 6

C. 8

D. 12

E. 16

Answer 1

E. 16

Explanation:

For this, we will use c and d to designate the values for the constant and the leading coefficient. The possible rational roots result from the combination of both the positive and negative values found in c/d.

First, c. c = -12. The factors of 12 are:

±1, ±2, ±3, ±4, ±6, ±12

Now d. d = 2. The factors of 2 are:

±1, ±2

Now to find the total possible rational roots we put c over d to give us:

±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2

That is 8 values, but since we have to also consider the negatives of each of them, that 8 becomes 16