Question

Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x2-x=-4
has.
a.two real solutions


b. no real or complex solutions


c. one real solution


d. two complex (nonreal)

Answer 1

Interpret the equation as 2x^2 − x = −4 → 2x^2 − x + 4 = 0.
Here a = 2, b = −1, c = 4. The discriminant Δ = b^2 − 4ac = 1 − 32 = −31 < 0, so there are two complex (nonreal) solutions.

(They are x = (1 ± i√31)/4.)
Answer: d. two complex (nonreal)