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). Further Maths GCSE Revision Revision Cards Books Factorising Quadratics Practice Questions. 5-a-day GCSE 9-1 5-a-day Primary 5-a-day Further Maths More. Step 3: Set that expansion equal to the constant term: `1 - u^2 = -15` Welcome Videos and Worksheets Primary 5-a-day. Im not done, though, because the original exercise told me to 'check', which means that I. These two values are the solution to the original quadratic equation. This is the easiest method of solving a quadratic equation as long as the binomial or trinomial is easily factorable. Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations: x + 2 0 or x + 3 0. Step 1: Take −1/2 times the x coefficient. How to Solve Quadratic Equations using Factoring Method.
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. (Similarly, when we substitute `x = -3`, we also get `0`.) Alternate method (Po-Shen Loh's approach) We check the roots in the original equation by 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 Factoring Quadratics A Quadratic Equation in Standard Form ( a, b, and c can have any value, except that a cant be 0. (iv) Solve the resulting linear equations (i) Bring all terms to the left and simplify, leaving zero on 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 The quadratic equation x 2 − 6 x + 9 = 0 has double roots of x = 3 (both roots are the same) 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 The solution of an equation consists of all numbers (roots) which make the equation true.Īll quadratic equations have 2 solutions (ie.
bx − 6 = 0 is NOT a quadratic equation because there is no x 2 term.must NOT contain terms with degrees higher than x 2 eg.Therefore, when solving quadratic equations by factoring, we must always have the equation in the form "(quadratic expression) equals (zero)" before we make any attempt to solve the quadratic equation by factoring. If the product of factors is equal to anything non-zero, then we can not make any claim about the values of the factors. We can only draw the helpful conclusion about the factors (namely, that one of those factors must have been equal to zero, so we can set the factors equal to zero) if the product itself equals zero. In particular, we can set each of the factors equal to zero, and solve the resulting equation for one solution of the original equation. So, if we multiply two (or more) factors and get a zero result, then we know that at least one of the factors was itself equal to zero. If the quadratic factors easily, this method is very quick. Put another way, the only way for us to get zero when we multiply two (or more) factors together is for one of the factors to have been zero. Methods to Solve Quadratic Equations: Factoring Square Root Property Completing the Square Quadratic Formula How to identify the most appropriate method to solve a quadratic equation. Zero-Product Property: If we multiply two (or more) things together and the result is equal to zero, then we know that at least one of those things that we multiplied must also have been equal to zero.