12.02 and 12.03 Determine the Discriminant

Front

What is the discriminant in a quadratic equation?

Back

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

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 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

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

Back

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

Front

How do you calculate the discriminant for the quadratic equation 2x² + 3x + 1?

Back

For the equation 2x² + 3x + 1, the discriminant is calculated as b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1.

Front

If the discriminant is 16, what can you conclude about the roots of the quadratic equation?

Back

If the discriminant is 16, you can conclude that the quadratic equation has two distinct real roots.

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

Solve the equation 2x² - 4x + 2 = 0 using the quadratic formula.

Back

Using the quadratic formula: x = (4 ± √(0)) / 4 = 1 (double root).

Front

What is the significance of the term 'complex roots' in relation to the discriminant?

Back

Complex roots occur when the discriminant is negative, indicating that the quadratic equation does not intersect the x-axis.

Front

How can you determine if a quadratic function crosses the x-axis using the discriminant?

Back

You can determine if a quadratic function crosses the x-axis by checking the discriminant: if it is positive, it crosses; if it is zero, it touches; if it is negative, it does not cross.