Question

Use the discriminant to describe the number and type of roots for the equation.

𝑟^2−3⁢𝑟/5+2/5=0 rational, irrational, or complex?

Answer 1

For r^2 − (3/5)r + 2/5 = 0, a = 1, b = −3/5, c = 2/5.

Discriminant Δ = b^2 − 4ac = (−3/5)^2 − 4(1)(2/5) = 9/25 − 40/25 = −31/25 < 0.

Since Δ < 0, the equation has two nonreal complex conjugate roots:
r = [−b ± √Δ]/(2a) = [3/5 ± i√31/5]/2 = 3/10 ± (i√31)/10.