Roots of Quadratics

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax^2 + bx + c. It is given by the formula D = b^2 - 4ac. The discriminant determines the nature of the roots of the quadratic equation.

Front

How does the discriminant indicate the nature of the roots?

Back

If D > 0, the quadratic has two distinct real roots. If D = 0, there is exactly one real root (a repeated root). If D < 0, the quadratic has two complex (non-real) roots.

Front

Calculate the discriminant of the quadratic equation 6x^2 - 5x + 1 = 0.

Back

1

Front

Calculate the discriminant of the quadratic equation 4x^2 + 7x + 2 = 0.

Back

17

Front

Find the discriminant of the quadratic equation 5x^2 + 2x + 1 = 0.

Back

-16

Front

What is the discriminant of the quadratic equation 2x^2 + 5x + 3 = 0?

Back

1

Front

Determine the discriminant of the quadratic equation 2x^2 - 3x + 1 = 0.

Back

1

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, which is 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 (non-real) roots.