Question

Find the value of the discriminant for the quadratic equation. Then describe the number and type of roots for the equation. Use the words rational, irrational, or complex to describe the roots.

5⁢𝑥^2−𝑥−1=0



discriminant:

number of roots:

type of root(s):

Answer 1

Discriminant: Δ = b^2 − 4ac = (−1)^2 − 4(5)(−1) = 1 + 20 = 21

Number of roots: 2 (since Δ > 0)

Type of root(s): irrational (two distinct real irrational roots, ±√21 gives nonrational values)