Quadratic Formula and Discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

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. If D > 0, there are 2 real solutions; D = 0 means 1 real solution; D < 0 indicates no real solutions.

Front

If the discriminant is positive, how many solutions does the quadratic equation have?

Back

2 real solutions.

Front

If the discriminant is zero, how many solutions does the quadratic equation have?

Back

1 real solution.

Front

If the discriminant is negative, how many solutions does the quadratic equation have?

Back

No real solutions.

Front

Solve using the quadratic formula: x² - 4x - 5 = 0

Back

x = 5, x = -1.

Front

What is the value of the discriminant for the equation 3x² + 6x + 2 = 0?

Back

D = 6² - 4(3)(2) = 36 - 24 = 12 (positive, so 2 real solutions).

Front

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

Back

x = 1/2, x = -2.

Front

What is the significance of the term 'b' in the quadratic formula?

Back

The term 'b' represents the coefficient of the linear term in the quadratic equation ax² + bx + c.

Front

What does 'a' represent in the quadratic formula?

Back

The term 'a' is the coefficient of the quadratic term in the equation ax² + bx + c.