Determine the type and number of solutions of 3x^2 + 6x + 4 = 0.

A) one real solution and one imaginary solution

B) one real solution

C) two real solutions

D) two imaginary solutions

D

given a quadratic in standard form : ax² + bx + c = 0

To determine the nature of the roots use the discriminant : b² - 4ac

• If b² - 4ac > 0, then two real and distinct roots

• If b² - 4ac = 0, then real and equal root

• I f b² - 4ac < 0, then roots are not real

here a = 3, b = 6 and c = 4

b² - 4ac = 6² - (4 * 3 * 4) = 36 - 48 = - 12

Hence 2 imaginary solutions