Discriminant

Front

What is the formula for the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac.

Front

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

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

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

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.

Front

Given the quadratic equation 5x² + x - 2 = 0, what is the discriminant?

Back

The discriminant is calculated as b² - 4ac = 1² - 4(5)(-2) = 1 + 40 = 41.

Front

For the quadratic equation 4x² - 8x = 3, identify the values of a, b, and c.

Back

a = 4, b = -8, c = -3.

Front

How do you determine the nature of the roots using the discriminant?

Back

Evaluate the discriminant: if > 0, two real roots; if = 0, one real root; if < 0, two imaginary roots.

Front

What is the discriminant of the quadratic equation x² + 7x + 13?

Back

The discriminant is -3, indicating 2 imaginary roots.

Front

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

Back

The solutions are complex and not real.

Front

What is the significance of the coefficients a, b, and c in the quadratic equation ax² + bx + c = 0?

Back

They represent the parameters that define the shape and position of the parabola.