Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of the quadratic equation: if positive, there are 2 real solutions; if zero, there is 1 real solution; if negative, there are no real solutions.

Front

What is the value of the discriminant for the equation x² - 4x + 4?

Back

The discriminant is 0, indicating that there is 1 real solution.

Front

How do you determine if a quadratic equation can be solved using the quadratic formula?

Back

A quadratic equation can be solved using the quadratic formula if it is in the standard form ax² + bx + c = 0, regardless of whether it can be factored.

Front

What is the significance of a positive discriminant?

Back

A positive discriminant indicates that the quadratic equation has 2 distinct real solutions.

Front

What is the significance of a negative discriminant?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Front

What is the significance of a zero discriminant?

Back

A zero discriminant indicates that the quadratic equation has exactly 1 real solution, also known as a repeated or double root.

Front

Solve the quadratic equation: x² - 6x + 9 = 0 using the quadratic formula.

Back

The solutions are x = 3 (double root).

Front

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

Back

It has 2 real solutions.

Front

What is the first step in using the quadratic formula?

Back

Identify the coefficients a, b, and c from the quadratic equation in the form ax² + bx + c = 0.