Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What are the values of a, b, and c in the equation 4x² - 8x - 3 = 0?

Back

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

Front

What is the leading coefficient in the equation y = x² + 5x + 7?

Back

The leading coefficient is 1.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots.

Front

How do you rearrange the equation 4x² - 8x = 3 to use the Quadratic Formula?

Back

Rearrange to 4x² - 8x - 3 = 0.

Front

What are the roots of the equation x² + 4x - 40 = -8?

Back

The roots are x = -8 and x = 4.

Front

What is the value of the discriminant for the equation 2x² + 2x - 12 = 0?

Back

The discriminant is 4 - 4(2)(-12) = 100.

Front

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

Back

A positive discriminant indicates that there are two distinct real roots.

Front

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

Back

A zero discriminant indicates that there is exactly one real root (a repeated root).

Front

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

Back

A negative discriminant indicates that there are no real roots (the roots are complex).