Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (D) represent in a quadratic equation?

Back

The discriminant (D) is the part of the quadratic formula under the square root, calculated as D = b² - 4ac. It determines the nature of the roots of the quadratic equation.

Front

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

Back

Two real solutions.

Front

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

Back

One real solution with a multiplicity of 2.

Front

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

Back

No real solutions; the solutions are imaginary.

Front

Calculate the discriminant for the quadratic equation: x² + 4x + 4.

Back

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

Front

What is the nature of the roots if the discriminant is -16?

Back

The roots are two imaginary solutions.

Front

For the quadratic equation 2x² - 3x + 1 = 0, what is the value of the discriminant?

Back

D = (-3)² - 4(2)(1) = 9 - 8 = 1. The discriminant is positive, indicating two real solutions.

Front

What does it mean if the discriminant is equal to 25?

Back

It means the quadratic equation has two distinct real solutions.

Front

How do you determine the number of solutions for the equation -3x² - 5x + 15 = 7?

Back

First, rewrite it as -3x² - 5x + 8 = 0. Then calculate the discriminant: D = (-5)² - 4(-3)(8) = 25 + 96 = 121. There are 2 solutions.