4.6 Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions (roots) 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 tell us about the roots of a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation: If D > 0, there are 2 distinct real roots; If D = 0, there is 1 real root (a repeated root); If D < 0, there are 2 complex (imaginary) roots.

Tags

CCSS.HSA-REI.B.4B

Front

Calculate the discriminant for the equation: x² + 5x + 6.

Back

D = b² - 4ac = 5² - 4(1)(6) = 25 - 24 = 1 (2 distinct real roots).

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of a discriminant equal to zero?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

Solve the quadratic equation using the formula: 3x² - 12x + 9 = 0.

Back

x = (12 ± √(0)) / 6 = 2 (one real solution).

Tags

CCSS.HSA-REI.B.4B

Front

What are the roots of the equation: x² - 4 = 0?

Back

x = ±2 (two distinct real roots).

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant is negative, what can we say about the roots?

Back

If the discriminant is negative, the quadratic equation has two complex (imaginary) roots.

Tags

CCSS.HSA-REI.B.4B

Front

Solve the quadratic equation: 2x² + 3x - 5 = 0 using the quadratic formula.

Back

x = (−3 ± √(49)) / 4 = 1 and -2.5 (two distinct real roots).

Tags

CCSS.HSA-REI.B.4B

Front

What is the value of the discriminant for the equation: 4x² + 4x + 1?

Back

D = 4² - 4(4)(1) = 16 - 16 = 0 (1 real root).

Tags

CCSS.HSA-REI.B.4B

Front

How do you determine the number of real solutions from the discriminant?

Back

Count the number of real solutions based on the discriminant: D > 0 = 2 real solutions, D = 0 = 1 real solution, D < 0 = 0 real solutions.

Tags

CCSS.HSA-REI.B.4B