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 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.

Front

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

Back

None.

Front

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

Back

Two.

Front

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

Back

-7.

Front

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

Back

One.

Front

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

Back

76.

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.

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).

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.