Question

use the discriminant to determine the number of solutions of the quadratic equation.
3x² + 6x = -3

the number of real solutions is .

Explanation:

Step1: Rewrite in standard form

$3x^2 + 6x + 3 = 0$

Step2: Identify a, b, c

$a=3,\ b=6,\ c=3$

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 6^2 - 4(3)(3)$
$\Delta = 36 - 36 = 0$

Step4: Interpret discriminant

A discriminant of 0 means one real solution.

Answer:

1