Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots of the equation.

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, but two complex (imaginary) roots.

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

Given the quadratic equation y = x² + 4x + 4, what is the value of the discriminant?

Back

The discriminant is 0, indicating one real root.

Front

In the quadratic equation y = x² + 5x + 7, identify the coefficients a, b, and c.

Back

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

Front

How do you calculate the discriminant for the quadratic equation x² + 2x - 63?

Back

Use the formula b² - 4ac: (2)² - 4(1)(-63) = 4 + 252 = 256.

Front

What is the nature of the solutions for the equation x² + 2x - 63 based on its discriminant?

Back

The discriminant is 256, which is positive, indicating 2 distinct real roots.

Front

If a quadratic equation has a discriminant of 0, how many x-intercepts does it have?

Back

It has 1 x-intercept.

Front

What is the formula for the discriminant?

Back

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