Question

what does the discriminant, $b^2 - 4ac$ in the quadratic formula indicate about the roots of a quadratic equation?

• it affects the coefficients of the quadratic equation.
• it indicates whether the roots are real or complex.
• it shows the degree of the polynomial.
• it changes the curve of the parabola.

Explanation:

The discriminant $\boldsymbol{b^2-4ac}$ from the quadratic formula determines the nature of a quadratic equation's roots:

1. If $b^2-4ac > 0$: Two distinct real roots
2. If $b^2-4ac = 0$: One repeated real root
3. If $b^2-4ac < 0$: Two complex conjugate roots

It does not affect coefficients, define the polynomial degree, or alter the parabola's curve shape.

Answer:

B. It indicates whether the roots are real or complex.