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 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

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

Calculate the discriminant for the equation: 2x² + 3x + 1 = 0

Back

D = 3² - 4(2)(1) = 9 - 8 = 1 (positive discriminant, two distinct real roots).

Front

Calculate the discriminant for the equation: x² - 4x + 4 = 0

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0 (zero discriminant, one real root).

Front

Calculate the discriminant for the equation: 3x² + 2x + 5 = 0

Back

D = 2² - 4(3)(5) = 4 - 60 = -56 (negative discriminant, two complex roots).

Front

What is the formula for the discriminant?

Back

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

Front

If the discriminant is 0, what can be said about the graph of the quadratic function?

Back

The graph of the quadratic function touches the x-axis at one point (the vertex) and does not cross it.

Front

For the quadratic equation y = x² + 6x + 10, what is the discriminant?

Back

D = 6² - 4(1)(10) = 36 - 40 = -4 (negative discriminant, two complex roots).