Can you help me with this Pre-Calculus problem?

Question

How do I find all the possible zeros of f (x)= 2x^3-x^2+3x-4

Answer 1

Using the Rational Root Theorem,

p: ±1, ±2, ±4

q: ±1, ±2

p/q: ±1, ±1/2, ±2, ±4

 

Using Synthetic Division,

1/ 2   -1   3   -4

           2   1    4

     2    1   4   0

 

2x² + x + 4 = 0

 

Use the quadratic formula to get your answer:

x = -1 ± √(1 - 32) 

              4

x = -1 ± √-31 

            4

x = -1 ± i√31

           4