Front

What is the discriminant of a quadratic equation?

Back

The discriminant is a value that determines the nature of the roots of a quadratic equation, calculated as b² - 4ac.

Front

How do you calculate the discriminant for the equation 6x² − 2x − 3 = 0?

Back

The discriminant is calculated as (-2)² - 4(6)(-3) = 4 + 72 = 76.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Front

What does a discriminant of zero indicate about the roots of a quadratic equation?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real root (a repeated root).

Front

Identify the values of a, b, and c in the quadratic equation 4x² – 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

Use the quadratic formula to solve 2x² + 2x - 12 = 0.

Back

The solutions are x = 2 and x = -3.

Front

What is the significance of the coefficients a, b, and c in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.