Solve a quadratic equation using the zero product property

Learning Objectives Define the Zero Product Property in their own words. Identify if a quadratic equation is in the correct form to apply the Zero Product Property. Rearrange a quadratic equation into standard form (ax^2 + bx + c = 0). Factor a quadratic expression to prepare it for the Zero Product Property. Apply the Zero Product Property to a factored quadratic equation to find all possible solutions. Solve the resulting linear equations to determine the roots of the original quadratic equation. Verify the solutions by substituting them back into the original equation. If you know that A × B = 0, what can you say for sure about A or B? 🤔 This one simple, powerful idea is the key to solving a huge class of equations! This tutorial will guide you through one of the most...

TermDefinitionExample Quadratic EquationA polynomial equation of the second degree, meaning it contains a term with a variable raised to the power of 2. Its general form is ax^2 + bx + c = 0.2x^2 - 5x - 3 = 0 is a quadratic equation. Standard FormThe form of a quadratic equation where all terms are on one side of the equation, set equal to zero: ax^2 + bx + c = 0, where a ≠ 0.The equation x^2 = 4x + 5 is not in standard form. The standard form is x^2 - 4x - 5 = 0. FactorAn algebraic expression that divides another expression evenly. When multiplied together, factors produce the original expression.(x - 3) and (x + 2) are factors of x^2 - x - 6, because (x - 3)(x + 2) = x^2 - x - 6. Factored FormA quadratic equation expressed as a product of its linear factors, set equal to zero.The factor...

The Zero Product Property If A \cdot B = 0, then A = 0 \text{ or } B = 0 \text{ (or both)}. This is the core principle. If the product of two or more factors is zero, then at least one of those factors must be equal to zero. We use this after factoring a quadratic equation to split it into simpler linear equations. Standard Form Requirement ax^2 + bx + c = 0 Before you can factor and apply the Zero Product Property, the quadratic equation must be in standard form. This means one side of the equation must be zero.