The Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value that determines the nature of the roots of a quadratic equation, given by the formula b² - 4ac.

Front

How many solutions does a quadratic equation have if the discriminant is positive?

Back

Two distinct real solutions.

Front

How many solutions does a quadratic equation have if the discriminant is zero?

Back

One real solution (a repeated root).

Front

How many solutions does a quadratic equation have if the discriminant is negative?

Back

No real solutions (the roots are complex).

Front

What is the formula for the discriminant of a quadratic equation ax² + bx + c = 0?

Back

b² - 4ac.

Front

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

Back

100.

Front

What does a positive discriminant indicate about the graph of a quadratic function?

Back

The graph intersects the x-axis at two points.

Front

What does a zero discriminant indicate about the graph of a quadratic function?

Back

The graph touches the x-axis at one point (vertex).

Front

What does a negative discriminant indicate about the graph of a quadratic function?

Back

The graph does not intersect the x-axis.

Front

Find the discriminant of the equation -2x² - x - 1 = 0.

Back

-7.