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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