Solving Quadratics with Complex Roots

Front

If b² - 4ac is negative, the quadratic equation has:

Back

Two imaginary solutions that are different.

Front

Solve for x: x² - 4x + 5 = 0

Back

x = 2 ± i.

Front

Solve for x: 3x² - 6x + 6 = 0

Back

x = 1 ± i.

Front

Solve for x: x² + 2x + 5 = 0

Back

x = -1 ± 2i.

Front

Solve for x: x² - 5x + 8 = 0

Back

x = (5 ± i√7)/2.

Front

What does the discriminant (b² - 4ac) indicate in a quadratic equation?

Back

It determines the nature of the roots: positive for two real solutions, zero for one real double solution, and negative for two imaginary solutions.

Front

Define complex roots in the context of quadratic equations.

Back

Complex roots are solutions that include imaginary numbers, occurring when the discriminant is negative.

Front

Solve for x: x² + 4x + 8 = 0

Back

x = -2 ± 2i.

Front

What is the general form of a quadratic equation?

Back

The general form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you find the roots of a quadratic equation using the quadratic formula?

Back

The roots can be found using x = (-b ± √(b² - 4ac)) / (2a).