quadratic formula alg

What is the quadratic formula used for?

To find the solutions (roots) of a quadratic equation, which is in the form $ax^2 + bx + c = 0$.

Which of the following represents the quadratic formula?

The quadratic formula is represented as $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Given the equation $2x^2 + 4x - 6 = 0$, what are the values of a, b, and c in the quadratic formula?

a = 2, b = 4, c = -6.

If the discriminant ($D = b^2 - 4ac$) is greater than 0, what does it indicate about the roots of the quadratic equation?

The equation has two distinct real roots.

If the discriminant is equal to 0, how many roots does the quadratic equation have?

The equation has exactly one real root (a repeated root).

If the discriminant is less than 0, what does it indicate about the roots of the quadratic equation?

The equation has no real roots, and the roots are complex.