![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis Edexcel Exam Papers OCR Exam Papers AQA Exam Papers. Use the information below to generate a citation. Maths revision video and notes on the topic of the quadratic formula. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. This last equation is the Quadratic Formula. When the Discriminant ( b24ac) is: positive, there are 2 real solutions. Plug these coefficients into the quadratic formula. Quadratic Equation in Standard Form: ax 2 + bx + c 0. X = − b ± b 2 − 4 a c 2 a x = − b ± b 2 − 4 a c 2 a To find the coefficients, use the standard form of a quadratic equation: a x 2 + b x + c 0. X = − b 2 a ± b 2 − 4 a c 2 a x = − b 2 a ± b 2 − 4 a c 2 a X + b 2 a = ± b 2 − 4 a c 2 a x + b 2 a = ± b 2 − 4 a c 2 aĪdd − b 2 a − b 2 a to both sides of the equation. Suppose ax² + 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. ![]() Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula. The formula for a quadratic equation is used to find the roots of the equation. Remember, to use the Quadratic Formula, the equation must be written in standard form, ax2 + bx + c 0. X + b 2 a = ± b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 Solve by using the Quadratic Formula: 5b2 + 2b + 4 0 5 b 2 + 2 b + 4 0. ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 These are the four general methods by which we can solve a quadratic equation. This derivation gives us a formula that solves any quadratic equation in standard form. ( x + b 2 a ) 2 = − c a + b 2 4 a 2 ( x + b 2 a ) 2 = − c a + b 2 4 a 2įind the common denominator of the right side and writeĮquivalent fractions with the common denominator. Answer: There are various methods by which you can solve a quadratic equation such as: factorization, completing the square, quadratic formula, and graphing. The left side is a perfect square, factor it. X 2 + b a x + b 2 4 a 2 = − c a + b 2 4 a 2 x 2 + b a x + b 2 4 a 2 = − c a + b 2 4 a 2 Make leading coefficient 1, by dividing by a.Ī x 2 a + b a x = − c a a x 2 a + b a x = − c a We start with the standard form of a quadratic equationĪnd solve it for x by completing the square.Ī x 2 + b x + c = 0 a ≠ 0 a x 2 + b x + c = 0 a ≠ 0
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