Solving Quadratics with Complex Roots

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are complex roots?

Back

Complex roots are solutions to polynomial equations that include imaginary numbers, typically expressed in the form a ± bi, where i is the imaginary unit.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of a quadratic equation: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

Solve for x: x² - 3x + 10 = 0

Back

x = (3 ± i√31)/2

Front

Solve for x: x² - 5x + 8 = 0

Back

x = (5 ± i√7)/2

Front

Solve for x: 3x² - 6x + 6 = 0

Back

x = 1 ± i

Front

Solve for x: x² - 5x + 10 = 0

Back

x = (5 ± i√15)/2

Front

Solve for x: x² + 4x + 8 = 0

Back

x = -2 ± 2i

Front

What is the significance of the imaginary unit i?

Back

The imaginary unit i is defined as √(-1) and is used to express complex numbers.