Quadratic Formula and 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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation. It indicates whether the roots are real or imaginary.

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.

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 (two imaginary solutions).

Tags

CCSS.HSA-REI.B.4B

Front

Calculate the discriminant for the equation: 3x² + 6x + 2 = 0.

Back

D = 6² - 4(3)(2) = 36 - 24 = 12 (positive, two real solutions).

Tags

CCSS.HSA-REI.B.4B

Front

Calculate the discriminant for the equation: x² - 4x + 4 = 0.

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0 (zero, one real solution).

Tags

CCSS.HSA-REI.B.4B

Front

Calculate the discriminant for the equation: 2x² + 4x + 5 = 0.

Back

D = 4² - 4(2)(5) = 16 - 40 = -24 (negative, no real solutions).

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of a positive discriminant?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of a zero discriminant?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

Tags

CCSS.HSA-REI.B.4B