Quadratic Formula

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?

Back

The discriminant (D) is the part of the quadratic formula under the square root: D = b² - 4ac. It indicates the nature of the roots of the quadratic equation.

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What does a positive discriminant indicate?

Back

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

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What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

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

Front

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

Back

The solutions are x = 2 and x = -3.

Front

What is the value of the discriminant for the equation 4x² + 6x - 4 = 0?

Back

The discriminant is 100.

Front

How many solutions does the equation 3x² + 2x + 1 = 0 have?

Back

It has no real solutions because the discriminant is negative.

Front

If the discriminant is 0, how many solutions does the quadratic equation have?

Back

It has one real solution.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is D = b² - 4ac.