The 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

How do you determine the number of real solutions using the discriminant?

Back

If the discriminant is positive, there are 2 real solutions. If it is zero, there is 1 real solution. If it is negative, there are no real solutions.

Front

Calculate the discriminant for the quadratic equation 4x² + 6x - 4 = 0.

Back

The discriminant is 100, indicating 2 solutions.

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real solutions.

Front

What is the discriminant of the equation -2x² - x - 1 = 0?

Back

The discriminant is -7.

Front

For the quadratic equation x² - 6x + 9 = 0, what is the discriminant and how many solutions does it have?

Back

The discriminant is 0, indicating 1 solution.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

If the discriminant is 0, what can be said about the vertex of the parabola?

Back

The vertex of the parabola touches the x-axis at one point, indicating a double root.

Front

What is the significance of the discriminant in graphing a quadratic function?

Back

The discriminant helps determine the number of x-intercepts (real solutions) of the quadratic function.

Front

How can you use the discriminant to predict the nature of the roots of a quadratic equation?

Back

By evaluating the discriminant: positive (2 real roots), zero (1 real root), negative (no real roots).