Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots 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: 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.

Front

Solve using the quadratic formula: 9x² = 4 + 7x

Back

x = 1.16 and x = -0.38.

Front

Solve using the quadratic formula: 2x² + 2x - 12 = 0

Back

x = 2 and x = -3.

Front

Determine the value of the discriminant for x² + 7x + 13 = 0.

Back

The discriminant is -3, indicating 2 imaginary roots.

Front

What is the discriminant of the equation x² - 6x + 9 = 0?

Back

The discriminant is 0, indicating 1 real root.

Front

What is the formula for the discriminant?

Back

The discriminant is given by D = b² - 4ac.

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 roots.

Front

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

Back

If the discriminant is zero, the quadratic equation has exactly 1 real root (a repeated root).

Front

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

Back

If the discriminant is negative, the quadratic equation has 2 complex (imaginary) roots.