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 of a quadratic equation indicate?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant is equal to -2, how many real solutions are there?

Back

None.

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant of the quadratic equation is equal to 4, how many real solutions are there?

Back

Two.

Tags

CCSS.HSA-REI.B.4B

Front

What is the value of the discriminant of -2x² − x − 1 = 0?

Back

-7.

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant of the quadratic equation is equal to 0, how many real solutions are there?

Back

One.

Tags

CCSS.HSA-REI.B.4B

Front

What is the value of the discriminant of 6x² − 2x − 3 = 0?

Back

76.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Tags

CCSS.HSA-REI.B.4B