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. It is given by the formula D = 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 two distinct real solutions.

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 solution (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 no real solutions, but two complex solutions.

Front

Given the quadratic equation 4x² - 8x = 3, identify the values of a, b, and c.

Back

a = 4, b = -8, c = -3.

Front

How do you determine if a number is rational or irrational?

Back

A number is rational if it can be expressed as a fraction of two integers. It is irrational if it cannot be expressed in this way.

Front

If the graph of a quadratic does not touch the x-axis, what can be said about its solutions?

Back

It has no real solutions.

Front

If the discriminant is equal to -2, how many real solutions does the quadratic equation have?

Back

No real solutions.

Front

What is the formula for calculating the discriminant?

Back

D = b² - 4ac.

Front

What is the significance of the discriminant in relation to the graph of a quadratic function?

Back

The discriminant helps determine the number and type of roots, which affects how the graph intersects the x-axis.