The discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

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 no real solutions, but two complex solutions.

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Front

How do you calculate the discriminant for the equation 6x² − 2x − 3 = 0?

Back

To calculate the discriminant, use the formula b² - 4ac. Here, a = 6, b = -2, and c = -3. The discriminant is (-2)² - 4(6)(-3) = 4 + 72 = 76.

Front

If a quadratic equation has a discriminant of 25, how many solutions does it have?

Back

It has 2 distinct real solutions, since the discriminant is positive.

Front

What is the significance of the discriminant in determining the nature of the roots of a quadratic equation?

Back

The discriminant helps determine whether the roots are real and distinct, real and equal, or complex.

Front

In the quadratic formula, what role does the discriminant play?

Back

In the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), the discriminant (b² - 4ac) determines the number and type of solutions.

Front

What is the discriminant of the quadratic equation x² + 4x + 4 = 0?

Back

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

Front

How can you tell if a quadratic equation has complex solutions using the discriminant?

Back

If the discriminant is negative, the quadratic equation has complex solutions.