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, given by the formula b² - 4ac.

Front

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

Back

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

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 complex (imaginary) 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 (a repeated root).

Front

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

Back

The discriminant is calculated as b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1 (positive, so two real solutions).

Front

For the quadratic equation y = x² + 4x + 4, what is the discriminant?

Back

The discriminant is b² - 4ac = 4² - 4(1)(4) = 16 - 16 = 0 (indicating one real solution).

Front

If the discriminant is 25, what type of solutions does the quadratic equation have?

Back

The discriminant of 25 indicates that the quadratic equation has two rational solutions.

Front

What is the formula for calculating the discriminant?

Back

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

Front

If the discriminant is negative, how many solutions does the quadratic equation have?

Back

If the discriminant is negative, the quadratic equation has two imaginary solutions.

Front

What is the significance of the discriminant in relation to the graph of a quadratic function?

Back

The discriminant helps determine the number of x-intercepts (real solutions) of the quadratic function's graph.