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. It is given by the formula D = b² - 4ac.

Front

How do you calculate the discriminant for the equation x² + 7x + 13 = 0?

Back

D = 7² - 4(1)(13) = 49 - 52 = -3.

Front

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

Back

A negative discriminant indicates that the quadratic equation has two non-real solutions or no real solutions.

Front

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

Back

A discriminant of zero indicates that the quadratic equation has exactly one real solution.

Front

How many real solutions does the equation 6x² − 2x − 3 = 0 have?

Back

The equation has 2 real solutions.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is D = b² - 4ac.

Front

If the discriminant is positive, what can be said about the solutions of the quadratic equation?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

In the quadratic equation y = x² + 5x + 7, identify the coefficients a, b, and c.

Back

a = 1, b = 5, c = 7.

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What happens to the graph of a quadratic equation when the discriminant is negative?

Back

When the discriminant is negative, the graph does not intersect the x-axis, indicating no real solutions.