Quadratic Formula and Complex Numbers

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 'completing the square' mean?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as √-1, and it is used to represent the square root of negative numbers.

Front

How do you simplify √-x?

Back

To simplify √-x, you can express it as i√x.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

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

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.

Front

How do you solve the equation x² + 6x - 13 = 3?

Back

First, make it equal to 0 by subtracting 3 from both sides: x² + 6x - 16 = 0.