Question

Find the discriminant and the number of real roots for this equation: 9x² - 12x + 4 = 0.

A) Discriminant = 0, 2 real roots
B) Discriminant > 0, 2 real roots
C) Discriminant < 0, 0 real roots
D) Discriminant > 0, 1 real root

Answer 1

The discriminant is equal to 0, which indicates that the quadratic equation has 2 real roots.

Step-by-step explanation:

To find the discriminant and the number of real roots for the equation 9x² - 12x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the discriminant can be found as D = b² - 4ac. In this case, a = 9, b = -12, and c = 4. Substituting these values into the formula, we get D = (-12)² - 4(9)(4) = 144 - 144 = 0.

Since the discriminant is equal to 0, this tells us that the quadratic equation has 2 real roots. So, the correct answer is Option A) Discriminant = 0, 2 real roots.