Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac, where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.

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 two complex (imaginary) 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, also known as a repeated or double root.

Front

Calculate the discriminant for the equation: 2x² + 3x + 1 = 0.

Back

The discriminant is b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1 (positive, two distinct real roots).

Front

Calculate the discriminant for the equation: x² - 4x + 4 = 0.

Back

The discriminant is b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0 (one real root, multiplicity of 2).

Front

Calculate the discriminant for the equation: x² + 2x + 5 = 0.

Back

The discriminant is b² - 4ac = 2² - 4(1)(5) = 4 - 20 = -16 (negative, two imaginary roots).

Front

If the discriminant of a quadratic equation is 25, how many solutions does it have?

Back

The quadratic equation has 2 distinct real solutions.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is D = b² - 4ac.

Front

For the quadratic equation y = x² + 4x + 4, what is the nature of the roots?

Back

The discriminant is 0, indicating one real root (double root).