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Therefore, x = − 1 More Solved Examples For You The below image illustrates the best use of a quadratic equation.ĭiscriminant = b 2 − 4ac = 22 − 4×1×1 = 0
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The quantity in the square root is called the discriminant or D. Just plug in the values of a, b and c, and do the calculations. We define it as follows: If ax 2 + bx + c = 0 is a quadratic equation, then the value of x is given by the following formula: This is the general quadratic equation formula. A method that will work for every quadratic equation. For such equations, a more powerful method is required. There are equations that can’t be reduced using the above two methods. This is known as the method of completing the squares. x – 3 = ☖ Which gives us these equations:.(x-3) 2 = 36 Take square root of both sides.Now we can write it as a binomial square: (b/2) 2 where ‘b’ is the new coefficient of ‘x’, to both sides as: x 2 – 6x + 9 = 27 + 9 or x 2 – 2×3×x + 32 = 36. Next, we make the left hand side a complete square by adding (6/2) 2 = 9 i.e. So dividing throughout by the coefficient of x 2, we have: 2x 2/2 – 12x/2 = 54/2 or x 2 – 6x = 27. In the next step, we have to make sure that the coefficient of x 2 is 1. In the standard form, we can write it as: 2x 2 – 12x – 54 = 0. Next let us get all the terms with x 2 or x in them to one side of the equation: 2x 2 – 12 = 54 Solution: Let us write the equation 2x 2=12x+54. Let us see an example first.Įxample 2: Let us consider the equation, 2x 2=12x+54, the following table illustrates how to solve a quadratic equation, step by step by completing the square. If we could get two square terms on two sides of the quality sign, we will again get a linear equation. In those cases, we can use the other methods as discussed below.īrowse more Topics under Quadratic Equationsĭownload NCERT Solutions for Class 10 Mathematics Completing the Square MethodĮach quadratic equation has a square term. This method is convenient but is not applicable to every equation. Solving these equations for x gives: x=-4 or x=1. Thus we have either (x+4) = 0 or (x-1) = 0 or both are = 0. For any two quantities a and b, if a×b = 0, we must have either a = 0, b = 0 or a = b = 0. Thus, we can factorise the terms as: (x+4)(x-1) = 0. Hence, we write x 2 + 3x – 4 = 0 as x 2 + 4x – x – 4 = 0. Consider (+4) and (-1) as the factors, whose multiplication is -4 and sum is 3. We do it such that the product of the new coefficients equals the product of a and c. Next, the middle term is split into two terms. Solution: This method is also known as splitting the middle term method. Examples of FactorizationĮxample 1: Solve the equation: x 2 + 3x – 4 = 0 Let’s see an example and we will get to know more about it. Hence, from these equations, we get the value of x. These factors, if done correctly will give two linear equations in x. Certain quadratic equations can be factorised. Scroll down the page for more Solve Quadratic Equation by Factoring Worksheets.The first and simplest method of solving quadratic equations is the factorization method. Some may require more complex factoring methods, or you may need to use the quadratic formula or completing the square to find the solutions.Ĭlick on the following worksheet to get a printable pdf document. Remember that not all quadratic equations can be easily factored. Check solutions: Substitute x = 2 and x = 3 back into the original equation.Rewrite down the equation as: x 2 − 5x + 6 = 0.Check if the solutions obtained in step 4 satisfy the original quadratic equation.Įxample: Solve the quadratic equation x 2 − 5x = -6.These solutions are the roots or solutions of the quadratic equation. This will give you two separate linear equations to solve. Set each of the binomial factors equal to zero.Look for two binomials whose product gives you the original quadratic expression. Write the quadratic equation in the form: ax 2+bx+c=0, where a, b, and c are constants.These are the steps to solve a quadratic equation by factoring: Solve Quadratic Equation by Factoring (rearrange, factor & solve).Solve Quadratic Equation by Factoring (factor & solve, a ≠ 1).Solve Quadratic Equation by Factoring (factor & solve, a = 1).
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Solve Quadratic Equation by Factoring (use zero product property).There are four sets of solving equations using factoring worksheets. How to solve quadratic equations using factoring? Solve Quadratic Equation (use quadratic formula)Įxamples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to solve quadratic equations by factoring.Solve Quadratic Equation (use factoring).There are two sets of solving quadratic equation worksheets: