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

If the discriminant is positive, how many real solutions does the quadratic equation have?

Back

Two real solutions.

Front

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

Back

One real solution.

Front

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

Back

No real solutions.

Front

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

Back

b² - 4ac.

Front

For the quadratic equation -2x² - x - 1 = 0, if the discriminant is -7, what can we conclude about its solutions?

Back

The equation has no real solutions.

Front

For the quadratic equation 6x² - 2x - 3 = 0, if the discriminant is 76, what can we conclude about its solutions?

Back

The equation has two real solutions.

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 (the vertex).

Front

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

Back

The graph does not intersect the x-axis.