Solving Quadratics with Complex Solutions

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are complex solutions in the context of quadratic equations?

Back

Complex solutions are solutions to quadratic equations that include imaginary numbers, typically expressed in the form a ± bi, where a and b are real numbers and i is the imaginary unit.

Front

How do you determine if a quadratic equation has complex solutions?

Back

A quadratic equation has complex solutions if its discriminant (b² - 4ac) is less than zero.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots of the equation.

Front

Solve for x: x² + 4 = 0

Back

x = ±2i

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

Convert the equation 3x - 2x² = 5 into standard form.

Back

-2x² + 3x - 5 = 0.

Front

Solve for x: 2x² - 8 = 0

Back

x = ±2√2.

Front

What are the zeros of the function f(x) = x² + 9?

Back

The zeros are ±3i.

Front

Solve for x: x² - 6x + 10 = 0

Back

x = 3 ± i.