The Quadratic Formula

The Quadratic Formula

Introduction to Quadratic Formula

• The Quadratic Formula is a method used to solve equations of the form ax^2 + bx + c = 0.
• It is expressed as: x = [-b ± sqrt(b^2 - 4ac)] / (2a)

Understanding Components of the Formula

• In the quadratic formula, a, b, and c represent coefficients in the quadratic equation.
• ‘a’ is the coefficient of x^2, ‘b’ is the coefficient of x, and ‘c’ is the constant term.
• The “+” and “-“ in the formula show that there can be two possible solutions for ‘x’, which can be real or complex numbers.

Implementing the Formula

• The first step in using the quadratic formula involvees identifying the coefficients a, b, and c in the quadratic equation.
• Next, substitute these coefficients into the formula to determine the roots of the equation.

Importance of the Discriminant

• The term under the square root sign (b^2 - 4ac) in the quadratic formula is called the discriminant.
• The discriminant assists in determining the nature of the roots of the quadratic equation.
• Specifically, if the discriminant is greater than 0, there are two distinct real roots; if it’s equal to 0, there is exactly one real root (also called a repeated root); and if it’s less than 0, there are two complex roots.

Checking your Solutions

• Always substitute your solutions back into the original equation to confirm that they truly satisfy the equation.
• Even if you obtain solutions that appear unexpected (like irrational or complex numbers), they might be absolutely correct depending upon the nature of the quadratic equation, so do not disregard them outright.

Remember: The quadratic formula provides a powerful tool for solving any quadratic equation, even those that cannot be factored simply.