Quadratic Formula & the Discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant indicate in 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 2 complex (imaginary) solutions.

Front

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

Back

1 Real Solution.

Front

What is the value of the discriminant for the equation 3x² + 6x + 2?

Back

The discriminant is b² - 4ac = 6² - 4(3)(2) = 36 - 24 = 12.

Front

Can the quadratic formula be used for any quadratic equation?

Back

True, the quadratic formula can be used to solve any quadratic equation, whether it can be factored or not.

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.

Front

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

Back

x = 2 (double root).

Front

What happens if the discriminant is negative?

Back

The quadratic equation has 2 Complex (imaginary) Solutions.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

The sum of the roots is -b/a and the product of the roots is c/a.

Front

How do you determine if a quadratic equation can be factored?

Back

If the discriminant is a perfect square, the quadratic can be factored.