Question

Describe the nature of the roots of the equation 8x^2-2x-1=0. a) 1 real rational root. b) 2 real irrational roots. c) 2 real rational roots. d) 2 imaginary conjugates.

Answer 1

I would solve (or try to) and examine the roots.

Answer 2

\[8x ^{2}-2x-1=0\]First is would attempt factoring (as it is easier for me than the quadratic formula)

Answer 3

Yes, !! It does factor.
(4x+1)(2x-1)=0
4x=-1, then x = -1/4 a real rational number (answer)
other solution
2x-1=0
2x=1
x=1/2 another real rational number (answer)

Answer 4

I realize the question was closed, but I believe this was your first question, and don't want you to become discouraged with open study. Welcome and good luck.