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).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

Two real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

One real solution with a multiplicity of 2.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

No real solutions; the solutions are imaginary.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The roots are two imaginary solutions.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

It means the quadratic equation has two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B