Solving Quadratics with Complex Solutions

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

Back

The discriminant indicates the nature of the roots of the quadratic equation: if > 0, two distinct real solutions; if = 0, one real solution; if < 0, two complex solutions.

Front

How do you convert a quadratic equation to standard form?

Back

To convert to standard form, rearrange the equation to the form ax² + bx + c = 0.

Front

Solve for x: 2x² - 3x + 4 = 0

Back

x = {-3+2i, -3-2i}

Front

What are complex solutions?

Back

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

Front

If b² - 4ac < 0, how many solutions does the quadratic equation have?

Back

The quadratic equation has two complex solutions.

Front

Solve -2x² + 4x = 9

Back

x = (2 - i√14)/2, (2 + i√14)/2

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror-image halves.

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).