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 D = b² - 4ac. It 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 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

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

Back

The discriminant is 0, calculated as D = 4² - 4(1)(4) = 0.

Front

How many x-intercepts does a quadratic function with a discriminant of 4 have?

Back

It has 2 x-intercepts.

Front

If a quadratic function has a discriminant of 25, how many solutions does it have?

Back

It has 2 solutions.

Front

What are the coefficients in the quadratic equation y = x² + 5x + 7?

Back

The coefficients are a=1, b=5, c=7.

Front

Can the quadratic formula be used to solve any quadratic equation?

Back

Yes, the quadratic formula can be used to solve any quadratic equation, whether it can be factored or not.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √D) / (2a), where D is the discriminant.