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 about the roots of 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

If the discriminant is zero, what can we say about the roots of the quadratic equation?

Back

If the discriminant is zero, the quadratic equation has exactly one real root, which is a repeated root.

Front

Calculate the discriminant for the equation: x² + 4x + 4.

Back

D = b² - 4ac = 4² - 4(1)(4) = 16 - 16 = 0.

Front

What is the nature of the roots for the equation: x² + 5x + 6?

Back

The discriminant is D = 5² - 4(1)(6) = 25 - 24 = 1, which is positive, indicating 2 distinct real roots.

Front

Solve the quadratic equation using the quadratic formula: 2x² - 4x - 6 = 0.

Back

x = (4 ± √(16 + 48)) / 4 = (4 ± √64) / 4 = (4 ± 8) / 4. Solutions: x = 3 or x = -1.

Front

True or False: The quadratic formula can be used for any quadratic equation, even those that can be factored.

Back

True.

Front

What is the value of the discriminant for the equation: 3x² + 2x + 1?

Back

D = 2² - 4(3)(1) = 4 - 12 = -8, indicating 2 imaginary roots.

Front

If a quadratic equation has a discriminant of 25, how many solutions does it have?

Back

It has 2 distinct real solutions.

Front

What is the first step in using the quadratic formula?

Back

Identify the coefficients a, b, and c from the quadratic equation in the form ax² + bx + c = 0.