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 D = b² - 4ac.

Front

How do you calculate the discriminant for the equation 5x² + x - 2 = 0?

Back

D = (1)² - 4(5)(-2) = 1 + 40 = 41.

Front

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

Back

A positive discriminant indicates that there are two distinct real solutions.

Front

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

Back

A zero discriminant indicates that there is exactly one real solution (a repeated root).

Front

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

Back

A negative discriminant indicates that there are no real solutions, but two complex solutions.

Front

What is the formula for the discriminant?

Back

D = b² - 4ac.

Front

If the discriminant is 76, how many real solutions does the quadratic equation have?

Back

The quadratic equation has two distinct real solutions.

Front

What is the discriminant of the equation 6x² - 2x - 3 = 0?

Back

D = (-2)² - 4(6)(-3) = 4 + 72 = 76.

Front

What does the discriminant tell us about the nature of the roots of a quadratic equation?

Back

The discriminant tells us the number and type of solutions (real or complex) of the quadratic equation.

Front

What is the significance of the value of the discriminant in graphing a quadratic function?

Back

The value of the discriminant helps determine the number of x-intercepts (real solutions) of the graph.