Step 1) Write the quadratic equation in standard form. If K is greater than zero, we know that it prossesses two. This number, x, must be a square root of K. To solve x2 K, we are required to find some number, x, that when squared produces K. Either will work as a solution.Įxample 2: Solve each quadratic equation using factoring. Quadratic equations of the form x2 K 0 can be solved by the method of extraction of roots by rewriting it in the form x2 K. Step 3) Use the zero-product property and set each factor with a variable equal to zero: We want to subtract 18 away from each side of the equation: See examples of using the formula to solve a variety of equations. Then, we plug these coefficients in the formula: (-b± (b²-4ac))/ (2a). First, we bring the equation to the form ax²+bx+c0, where a, b, and c are coefficients. Use the zero-product property and set each factor with a variable equal to zeroĮxample 1: Solve each quadratic equation using factoring. The quadratic formula helps us solve any quadratic equation.Place the quadratic equation in standard form.In either scenario, the equation would be true:Ġ = 0 Solving a Quadratic Equation using Factoring To do this, we set each factor equal to zero and solve:Įssentially, x could be 2 or x could be -3. This means we can use our zero-product property. The result of this multiplication is zero. In this case, we have a quantity (x - 2) multiplied by another quantity (x + 3). We can apply this to more advanced examples. Y could be 0, x could be a non-zero number X could be 0, y could be a non-zero number The zero product property tells us if the product of two numbers is zero, then at least one of them must be zero: This works based on the zero-product property (also known as the zero-factor property). Suppose ax + bx + c 0 is the quadratic equation, then the formula to find the roots of this equation will be: x -b (b2-4ac)/2a. Since quadratics have a degree equal to two, therefore there will be two solutions for the equation. When a quadratic equation is in standard form and the left side can be factored, we can solve the quadratic equation using factoring. The formula for a quadratic equation is used to find the roots of the equation. Then, we do all the math to simplify the expression. To use the Quadratic Formula, we substitute the values of a, b, and c into the expression on the right side of the formula. For these types of problems, obtaining a solution can be a bit more work than what we have seen so far. The solutions to a quadratic equation of the form a x 2 + b x + c 0, a 0 are given by the formula: x b ± b 2 4 a c 2 a. Some examples of a quadratic equation are:ĥx 2 + 18x + 9 = 0 Zero-Product Property Up to this point, we have not attempted to solve an equation in which the exponent on a variable was not 1. Generally, we think about a quadratic equation in standard form:Ī ≠ 0 (since we must have a variable squared)Ī, b, and c are any real numbers (a can't be zero) A quadratic equation is an equation that contains a squared variable and no other term with a higher degree. We will expand on this knowledge and learn how to solve a quadratic equation using factoring. A quadratic expression contains a squared variable and no term with a higher degree. ![]() Over the course of the last few lessons, we have learned to factor quadratic expressions.
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