Question

Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number solutions does the equation have?

Discriminant = b2-4ac

0
1
2
12

Answer 1

First put in standard form: x^2 + 4x + 1 = −3 → x^2 + 4x + 4 = 0, so a = 1, b = 4, c = 4.

Discriminant = b^2 − 4ac = 4^2 − 4(1)(4) = 16 − 16 = 0.

Since the discriminant is 0, there is exactly 1 real solution (a repeated root).