Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula ax² + bx + c = 0, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

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

Front

What does a discriminant of zero indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex (imaginary) roots.

Front

Calculate the discriminant for the quadratic equation: 2x² + 4x + 2.

Back

The discriminant is 4 - 4(2)(2) = 4 - 16 = -12 (2 imaginary roots).

Front

For the quadratic equation x² - 6x + 9, what is the discriminant?

Back

The discriminant is 36 - 36 = 0 (1 real root with a multiplicity of 2).

Front

If the discriminant is 25, how many solutions does the quadratic have?

Back

The quadratic has 2 real and distinct solutions.

Front

What is the formula to calculate the discriminant?

Back

The formula is D = b² - 4ac.

Front

Identify the leading coefficient in the quadratic equation: 3x² + 2x - 5.

Back

The leading coefficient is 3.

Front

In the equation y = x² + 5x + 7, what are the values of a, b, and c?

Back

a = 1, b = 5, c = 7.