Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots.

Front

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

Back

2 real solutions.

Front

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

Back

1 real repeated solution.

Front

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

Back

0 real solutions (2 imaginary solutions).

Front

What does a discriminant of 25 indicate about the roots of the quadratic equation?

Back

It indicates that there are 2 distinct real roots.

Front

What does a discriminant of -3 indicate about the roots of the quadratic equation?

Back

It indicates that there are 2 imaginary roots.

Front

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

Back

0 (the roots are real and repeated).

Front

How do you calculate the discriminant for the quadratic equation ax² + bx + c?

Back

Use the formula b² - 4ac.

Front

What does the discriminant tell us about the nature of the roots?

Back

It tells us the number and type of solutions (real or imaginary).

Front

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

Back

The graph intersects the x-axis at two points.