2=0 This solution is nonsense so we discard it. Now we can set each factor equal to zero using the zero product rule. Make sure the equation is in standard form: ax2 + bx + c 0. Verify the factors using the distributive property of multiplication. How to: Use the Quadratic Formula to Solve an Equation. Fill in the rest of the binomials with the factors we found. Written in standard form, ax2 + bx + c 0 where a, b, and c are real numbers and a 0, any quadratic equation can be solved using the quadratic formula: x b ± b2 4ac 2a. Example 3: Find the quadratic equation having the roots 5 and 8 respectively. There are more factors that will give -45, but we have found the ones that sum to -4, so we will stop. But in instances when it cannot be solved by factorization, the quadratic formula is used. We want our factors to have a product of -45 and a sum of -4: Factors whose product is -45 We do this because 45 is negative and the only way to get a product that is negative is if one of the factors is negative. Using the shortcut for factoring we will start with the variable and place a plus and a minus sign in the binomials. Free quadratic equation factoring calculator - Solve quadratic equations using factoring step-by-step. If we can factor the polynomial, we will be able to solve. Note how we changed the signs when we factored out a negative number. Each term is divisible by 2, so we can factor out -2. This idea is called the zero product principle, and it is useful for solving polynomial equations that can be factored. You can further review the Principle of Zero Products here.Įach term has a common factor of t, so we can factor and use the zero product principle. Rewrite each term as the product of the GCF and the remaining terms. Solving by factoring depends on the Principle of Zero Products. What if we told you that we multiplied two numbers together and got an answer of zero? What could you say about the two numbers? Could they be 2 and 5? Could they be 9 and 1? No! When the result (answer) from multiplying two numbers is zero, that means that one of them had to be zero. We cover factoring in an earlier module of this course and you can sharpen your skills there. Note that we will not spend a lot of time explaining how to factor in this section. Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. Often the easiest method of solving a quadratic equation is by factoring. Where a, b, and c are real numbers, and if a\ne 0, it is in standard form.
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