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Solving Quadratic Equations Before we learn to solve quadratic equations, we need to remember an important property! Zero Product Property If ab = 0, then a = 0 or b = 0. a and b are real numbers (“factors”) Examples: a2= 0, then a = 0 3b = 0 then b = 0 a(a + 2) = 0, then a = 0 or a +2 = 0 SO… a = 0 or a = -2. Solving Quadratics Let’s learn how to solve quadratics by factoring the greatest common factor! When solving by factoring the GCF, the quadratic equation will look a certain way! The quadratic equation will have two types of terms: A quadratic term and a linear term. ax bx 0 2 Examples 4w 2w 2 5t 3t 0 2 OK, so how do we solve quadratic equations that look this way?!!! Solve by factoring GCF Solve 4w 2w 2 Step 1: Make one side zero, if not already. 4w 2w 0 Step 2: Factor out the GCF. 2w(2w 1) 0 Step 3: Set each factor to zero and solve for the variable. 2w 1 0 2 2w 0 w0 OR 1 w 2 Let’s Practice! You Try It! Solve 5t 3t 0 2 t (5t 3) 0 Factor the GCF! t 0 or 5t 3 0 3 t 0 or t 5 YOU DID IT! Hooray!!! THE END