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.

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: D > 0 means 2 real solutions, D = 0 means 1 real solution, and D < 0 means no real solutions.

Front

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

Back

D = b² - 4ac = (-4)² - 4(1)(4) = 0.

Front

What is the value of the discriminant for the equation: 2x² + 3x + 1 = 0?

Back

D = b² - 4ac = (3)² - 4(2)(1) = 1.

Front

How many solutions does the equation x² + 2x + 1 = 0 have?

Back

The discriminant is 0, so there is 1 solution.

Front

What is the discriminant of the equation: 5x² - 3x + 2 = 0?

Back

D = (-3)² - 4(5)(2) = 9 - 40 = -31, so there are no real solutions.

Front

If the discriminant is positive, what can we conclude about the roots?

Back

If the discriminant is positive, the quadratic equation has 2 distinct real solutions.

Front

What is the discriminant of the equation: 4x² + 4x + 1 = 0?

Back

D = (4)² - 4(4)(1) = 16 - 16 = 0, so there is 1 real solution.

Front

For the quadratic equation 3x² + 6x + 2 = 0, what is the discriminant?

Back

D = (6)² - 4(3)(2) = 36 - 24 = 12.

Front

What does a discriminant of 0 indicate about the roots of a quadratic equation?

Back

A discriminant of 0 indicates that the quadratic equation has exactly 1 real solution (a repeated root).