Quadratic Formula Examples Quadratic Formula Examples A Quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the form Ax2 + bx + c = 0 When you're solving quadratics in your homework, you can often get a "hint" as to the "best" method to use, based on the topic and title of the section. For instance, if you're working on the homework in the "Solving by Factoring" section, then you know that you're supposed to solve by factoring. But in the chapter review and on the test, you don't know which section the quadratic came from. Which method should you use? You could use the Quadratic Formula for everything, but the Formula can be "overkill". For example: Solve (x + 1)(x – 3) = 0. This is a quadratic, and I'm supposed to solve it. I could multiply the left-hand side, simplify to find the coefficients, plug them into the Quadratic Formula, and chug away to the answer. Know More About :- Addition and Multiplication property of Equality
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But why would I? I mean, for heaven's sake, this is factorable, and they've already factored it and set it equal to zero for me. While the Quadratic Formula would give me the correct answer, why bother with it? Instead, I'll just solve the factors: (x + 1)(x – 3) = 0 x + 1 = 0 or x – 3 = 0 x = –1 or x = 3 The solution is x = –1, 3 Solve x2 + x – 4 = 0. This one doesn't factor (since there are no factors of (1)(–4) = –4 that add to +1), and this isn't formatted as "(squared part) equals (a number)", so I can't use square-rooting to solve. This leaves me with completing the square (yuck!) or the Quadratic Formula. I'll use the Formula: The solution is Solve x2 – 3x – 4 = 0. x2 – 3x – 4 = 0 (x + 1)(x – 4) = 0 x + 1 = 0 or x – 4 = 0 x = –1 or x = 4 The solution is x = –1, 4 Solve x2 – 4 = 0. This quadratic has just two terms, and nothing factors out of both, so it's a difference of squares (so I can factor) or it can be reformatted as "(squared part) equals (a number)" so I can square-root both sides. In this case, I can factor: x2 – 4 = 0 (x + 2)(x – 2) = 0 x + 2 = 0 or x – 2 = 0 x = –2 or x = 2 The solution is x = ± 2 Read More About :- Solving Rational Expressions
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Thank You
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