Quadratic Equations

Solving Quadratic Equations Using the Quadratic Formula

Quadratic equations are polynomial equations of degree two, typically written in the standard form ax2 + bx + c = 0. The quadratic formula provides a systematic method for finding the solutions (roots) of any quadratic equation.

• Quadratic Formula: The solutions to the equation are given by:

• Discriminant: The expression under the square root, , is called the discriminant. It determines the nature of the roots:

  • If , there are two distinct real solutions.

  • If , there is one real solution (a repeated root).

  • If , there are two complex solutions.

Example: Solve

• Identify coefficients: , ,

• Apply the quadratic formula:

• Solution Set:

Key Points:

• Always write the quadratic equation in standard form before applying the formula.

• Simplify the radical and the final answer as much as possible.

• Use i to represent the imaginary unit when the discriminant is negative.