Question

Determine the number and the nature of the solutions to 3x^2 + 5x + 2 = 0.

2 rational roots

2 irrational roots

2 complex conjugates

1 rational root

Answer 1

Discriminant Δ = 5^2 − 4·3·2 = 25 − 24 = 1 > 0 and is a perfect square, so there are two distinct rational real roots.

They are x = (−5 ± 1)/(2·3) = −1 and −2/3.