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

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 negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex 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, also known as a repeated or double root.

Front

Calculate the discriminant for the equation 2x² + 4x + 2 = 0.

Back

D = 4² - 4(2)(2) = 16 - 16 = 0.

Front

Given A = 1, B = -3, and C = 2, find the discriminant.

Back

D = (-3)² - 4(1)(2) = 9 - 8 = 1.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Rewrite the equation x² - 4x + 4 = 0 in standard form.

Back

The equation is already in standard form: x² - 4x + 4 = 0.

Front

If the discriminant of a quadratic equation is 76, what can be said about its roots?

Back

The quadratic equation has two distinct real roots.

Front

What is the discriminant for the equation 5x² + x - 2 = 0?

Back

D = 1² - 4(5)(-2) = 1 + 40 = 41.