Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Choose the most efficient method for solving a quadratic equation
Problem
Use this decision rule: \((1)\) zero-product property if already factored and equal to \(0\); \((2)\) square-root property if an isolated square equals a constant; \((3)\) factoring if a short integer factorization is visible; otherwise \((4)\) quadratic formula. For \((x-2)(x+7)=0\), which complete response correctly applies the decision rule?
Big Picture
What this problem is really about
Method choice should use the equation’s current structure before doing any unnecessary algebra. We’ll scan the decision rule in order, recognize that this equation is already a product equal to zero, and apply the first matching method to both factors, checking each result directly in the original product.
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