Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c, given by the formula b² - 4ac.

Front

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

Back

A positive discriminant indicates that the quadratic equation has 2 distinct real 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 1 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 the quadratic equation has 2 complex (imaginary) roots.

Front

If the discriminant equals 49, how many and what type of roots does the quadratic equation have?

Back

The quadratic equation has 2 real rational roots.

Front

What is the formula for calculating the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

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

Back

The value of the discriminant is 0.

Front

When the discriminant is zero, how many solutions does the quadratic equation have?

Back

When the discriminant is zero, there is 1 real solution.

Front

When the discriminant is negative, how many solutions does the quadratic equation have?

Back

When the discriminant is negative, there are 2 imaginary solutions.

Front

What type of roots does a quadratic equation with a positive discriminant have?

Back

A quadratic equation with a positive discriminant has 2 real irrational roots or 2 real rational roots.