Different ways to solve quadratic equations
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i.e., Get all the terms of to one side (usually to left side) of the equation such that the other side is 0. Step – 1: Get the equation into standard form.The step-by-step process of solving quadratic equations by factoring is explained along with an example where we will solve the equation x 2 – 3x + 2 = 0. Solving quadratic equations by factoring is one of the famous methods used to solve quadratic equations. Now, we will learn the methods of solving the quadratic equations in each of the above-mentioned methods. Thus, the roots of the equation are 0 and -11. Thus, the roots of the equation are 0 and 5. The process is explained with examples below. To solve this type of equation, we simply factor x out from the left side, set each of the factors to zero, and solve. In a quadratic equation ax 2 + bx + c = 0, if the term with c is missing then the equation becomes ax 2 + bx = 0.
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(note that these are imaginary (or) complex numbers). Thus, the roots of the equation are 6i and -6i. Thus, the roots of the equation are 2 and -2. This can be solved by taking square root on both sides. In a quadratic equation ax 2 + bx + c = 0, if the term with b is missing then the equation becomes ax 2 + c = 0. Solving quadratic equations by quadratic formulaĪpart from these methods, there are some other methods that are used only in specific cases (when the quadratic equation has missing terms) as explained below.Solving quadratic equations by graphing.Solving quadratic equations by completing the square.Solving quadratic equations by factoring.But how to find them if they are not given? There are different ways of solving quadratic equations. Thus, x = 1 and x = 2 are the roots of x 2 – 3x + 2 = 0. For example, one can easily see that x = 1 and x = 2 satisfy the quadratic equation x 2 – 3x + 2 = 0 (you can substitute each of the values in this equation and verify). Since the degree of the quadratic equation is 2, it can have a maximum of 2 roots. The value(s) that satisfy the quadratic equation is known as its roots (or) solutions (or) zeros. Solving quadratic equations means finding a value (or) values of the variable which satisfy the equation. Solving Quadratic Equations by Quadratic Formula.Solving Quadratic Equations by Graphing.Solving Quadratic Equations by Completing Square.Solving Quadratic Equations by Factoring.