Solving Quadratic Equations

Solving Quadratic Equations

Basic Concepts

• A quadratic equation is of the form axe^2 + bx + c = 0, where a, b, and c are constants and ‘a’ should not be equal to zero.
• Roots of the quadratic equation can be real or complex.

Methods to Solve the Quadratic Equation

Factoring

• If a quadratic equation can be factored, it’s possible to set each set of parentheses equal to zero and solve.

Completing the Square

• This method involves making the quadratic equation into a perfect square trinomial, then solving that equation.

Quadratic Formula

• The Quadratic Formula, x = [-b ± sqrt(b^2 - 4ac)]/2a, can be used to solve any quadratic equation.

Types of Solutions

Real and Equal Roots

• A quadratic equation has real and equal roots if b^2 - 4ac = 0.

Real and Distinct Roots

• A quadratic equation has real and distinct roots if b^2 - 4ac > 0.

Complex or Imaginary Roots

• A quadratic equation has complex/imagination roots if b^2 - 4ac < 0.

Nature of Roots

• Depending on the discriminant (delta, Δ), b^2 - 4ac, we can determine the nature of roots without actually finding the roots.

Remember: The practise of solving different types of quadratic equations will help enforce understanding and application of these concepts.