Quadratic Equations with Real or 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 the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have two real solutions, one real solution (a repeated root), or two complex solutions.

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.

Front

What does the discriminant (b² - 4ac) indicate?

Back

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

Front

Solve for x: x² = -121

Back

x = ± 11i

Front

Solve for x: x² + 6x + 13 = 0

Back

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

Front

How many solutions does a quadratic equation have based on its degree?

Back

A quadratic equation has 2 solutions.

Front

Identify the zeros of the graph: y = x² - 2x - 3

Back

The zeros are (-1, 0) and (3, 0).

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at x = -b/(2a) in the equation ax² + bx + c.

Front

What is the axis of symmetry in a quadratic function?

Back

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