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Step 5: Substitute either value (we'll use `+4`) into the `u` bracket expressions, giving us the same roots of the quadratic equation that we found above:įor more on this approach, see: A Different Way to Solve Quadratic Equations (video by Po-Shen Loh). \(()() 0\) By the zero-factor property, at least one of the factors must be zero, so, set each of the factors equal to 0 and solve for the variable. \(ax2 + bx + c 0\) Factor the quadratic expression. Step 3: Set that expansion equal to the constant term: `1 - u^2 = -15` Set the equation equal to zero, that is, get all the nonzero terms on one side of the equal sign and 0 on the other. This is because when we square a solution, the result is always positive. Step 1: Take −1/2 times the x coefficient. When solving quadratic equations by taking square roots, both the positive and negative square roots are solutions to the equation. The following approach takes the guesswork out of the factoring step, and is similar to what we'll be doing next, in Completing the Square. We could have proceded as follows to solve this quadratic equation. Further Maths GCSE Revision Revision Cards Books Solving Quadratics: Factorising Textbook Exercise. 5-a-day GCSE 9-1 5-a-day Primary 5-a-day Further Maths More. Welcome Videos and Worksheets Primary 5-a-day. (Similarly, when we substitute `x = -3`, we also get `0`.) Alternate method (Po-Shen Loh's approach) The Corbettmaths Textbook Exercise on Solving Quadractics: Factorising. The first step, like before, is to isolate the term that has the variable squared. Notice that the quadratic term, x, in the original form ax 2 k is replaced with (x h). We can use the Square Root Property to solve an equation of the form a(x h) 2 k as well.
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We check the roots in the original equation by Solve Quadratic Equations of the Form a(x h) 2 k Using the Square Root Property. Now, if either of the terms ( x − 5) or ( x + 3) is 0, the product is zero. (v) Check the solutions in the original equation (iv) Solve the resulting linear equations 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. (i) Bring all terms to the left and simplify, leaving zero on The solutions to a quadratic equation of the form ax2 + bx + c 0, a 0 are given by the formula: x b ± b2 4ac 2a. Using the fact that a product is zero if any of its factors is zero we follow these steps: If you need a reminder on how to factor, go back to the section on: Factoring Trinomials. Solving a Quadratic Equation by Factoringįor the time being, we shall deal only with quadratic equations that can be factored (factorised). This can be seen by substituting x = 3 in the x2 7x + 12 0 The equation is already set equal to 0 (x 3)(x 4) 0 Factor. The quadratic equation x 2 − 6 x + 9 = 0 has double roots of x = 3 (both roots are the same) (We will show the check for problem 1.) Example 10.3.1. In this example, the roots are real and distinct. This can be seen by substituting in the equation: (We'll show below how to find these roots.) The quadratic equation x 2 − 7 x + 10 = 0 has roots of In order to master the techniques explained here it is vital that you. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs.
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The solution of an equation consists of all numbers (roots) which make the equation true.Īll quadratic equations have 2 solutions (ie. This unit is about the solution of quadratic equations.