![]() If a=1, then no coefficient appears in front of x^2. Remember, the standard form of a quadratic is:įor more information about forms of quadratics, check out our article on the different forms of quadratics. For our purpose, a simple quadratic means a quadratic where a=1. The x-intercepts can also be referred to as zeros, roots, or solutions. When you are asked to “solve a quadratic equation”, you are determining the x-intercepts. Return to the Table of Contents Factoring Quadratic Equations Examplesīefore things get too complicated, let’s begin by solving a simple quadratic equation. …we are simply saying that when we multiply (x-r_1) and (x-r_2), we will get the product ax^2+bx+x. Likewise, when we factor the standard from of a quadratic equation: Factors are terms that, when multiplied together, produce the original number or expression.Factoring a number or expression means breaking it into separate factors. ![]() There are other ways to factor 12, as well, such as using the factors 4 and 3 instead. The numbers 6 and 2 are factors of 12 because multiplying 6 and 2 gives the product of 12. Solving a Quadratic Equation Using Completing the Squareīefore we dig deep into factoring quadratic equations, let’s remember what factors are by looking at numerical examples.Determine a Quadratic Equation Given Its Roots.Solving Quadratic Equations by Factoring: World Problems.Factoring Trinomial with The Box Method.Video Examples of Factoring Quadratic Equation.Solving Quadratic Equations with the “AC Method”.Imaginative thing and Problem Solving are important skills for people in every field, and Professor Po-Shen Lou has shown us through developing this method that these skills are not something most people have mastered. However, none of us persisted through the problem to think about quadratic equations as such. This method turns out to be so simple and fun, I think many people could have figured it out. So, the final answer for the roots is x = (-3 + √2) and x = (-3 - √2). Fortunately, solving the product equation leads us to z = ±√2. Solving the sum equation z cancels out (whoops). Remember, from factoring, that the roots must add up to 6 and multiple to 7 so Therefore, the roots can be written as (-3 + z) and (-3 - z). Now, the parabola is symmetric on both sides of the vertex, and the two roots would be on opposite sides of the parabola a particular distance 'z' away. ![]() The vertex of a parabola is -B/2, where B is the coefficient of the term 'x' so the vertex of this parabola is -(6/2) = -3. He visualized this quadratic equation as a parabola. Po-Shen Lou didn't stop trying to find factors. I modified the previous equation by just a little but it has serious impacts because you won't be able to find two factors that add up to 6 and multiply to 7! This is where we give up on factoring and try Completing the Square or the Quadratic Formula. ![]() However, what if I ask you to find the roots of the equation -> x^2 + 6x + 7 = 0 And hence, after factoring, you get the two roots as x = -5 and x = -1. Let me demonstrate factoring:įor factoring, we need to find two numbers that add up to 6 and multiply to 5. I prefer factoring over the other two, lengthier methods. Humans have used it for thousands of years (Babylonians, Greeks)! Solving a quadratic equation has required one of the following three techniques The Quadratic Formula is something that every student has used since middle school. On October 13th, 2019, I was eating one of the most magnificent piece of pizza, a reward for completing the past exam week.Īt the very moment of my first bite, about 400 miles away, Po-Shen Lou, professor of Mathematics at the Carnegie Melon University, hit submit for a paper entitled 'A Simple Proof of the Quadratic Formula'. ![]()
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