Guided Example #1 - Quadratic Formula

Guided Example

State the value of the discriminant and the number of real solutions for $4 x^{2} + 12 x + 9 = 0$ .

a. Discriminant 288, two real solutions
b. Discriminant -288, no real solutions
c. Discriminant 0, one real solutions
d. None of the above

The correct answer is C. To see why, view each of the steps below.

Step 1

Find the value of $b^{2} - 4 a c$ using $a = 4, b = 12, c = 9$ ; the value of the discriminant is $b^{2} - 4 a c = 12^{2} - 4 (4) (9) = 0$ . So the equation has one real solution.

All Steps

Find the value of

$b^{2} - 4 a c$ using

$a = 4, b = 12, c = 9$ ; the value of the discriminant is

$b^{2} - 4 a c = 12^{2} - 4 (4) (9) = 0$ . So the equation has one real solution.