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 is the standard form of a quadratic equation?

Back

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

Front

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

Back

A quadratic equation has 2 solutions based on its degree.

Front

What does the discriminant (b² - 4ac) indicate about the solutions of a quadratic equation?

Back

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

Front

What are complex solutions in the context of quadratic equations?

Back

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

Front

What is the significance of the ± symbol in the quadratic formula?

Back

The ± symbol indicates that there are two possible solutions for x when solving a quadratic equation.

Front

Can a quadratic equation have complex solutions?

Back

Yes, a quadratic equation can have complex solutions if the discriminant is less than zero.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation 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 a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the role of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.