There are many different subjects under mathematics. Mathematics is known to be a collection of various formula and methods which guide you towards the right answers of the questions. Quadratic equations are some of the most important parts of algebraic math. There are many students who find difficulty in solving quadratic equations. Therefore in this content we will be talking about some simple ways of learning to solve such equations. Quadratic equation is also known as a polynomial equation with a single variable, in this equation the variable with highest exponent is always 2. Usually when it comes to the methods of solving these equations, there can be mainly three ways of doing this. These are 1.) By factoring the quadratic equation, 2.) Using the quadratic formula, and 3.) By completing the square. Therefore this content will be covering some of these for you. Quadratic formula is known to be one of the easiest ways of solving quadratics. However we will be starting by factoring the equation. Let’s solve something
It is very important to know about how to factor a quadratic equation as this is going to hold great importance further in this topic. You are told to find the values of x for a given equation to be true. For example: solve (x-3)(x-4)= 0 Actually, this equation has been already factored. So then how will you get the answers to the equation? According to the zero factor principle, at least one of the factors in the equation s should be equal to zero. Thus, x-3= 0 Or x-4= 0 Thus now they are in the form of a simple linear equation and can now be easily solved. Now we get, x = 3 or x = 4 Here the “or” indicates that the value of x can be either 3 or 4. And this is the correct solution you were looking for. Therefore it can be said that solving quadratic equations is easy by factoring the equation. Now an important thing to be discussed here is the verification of the solution that you’ve got from the above steps. Sometimes, factoring is not able to bring out the correct solutions for the equations. Therefore it is very important to cross check these in order to ensure accuracy. Foe the example solved above you needs to follow the following steps: Check x =3 in (x – 3) (x – 4) = 0: ([3] – 3) ([3] – 4)? =? 0 {putting the value of x in the equation as 3} (3 – 3)(3 – 4)? =? 0 Then solving these further we get, (0)(- 1)? =? 0 thus, 0=0 Hence proved correct (LHS = RHS) Now similarly check x = 4 in (x – 3)(x – 4) = 0: It will be solved like: ([4] – 3) ([4] – 4)? =? 0 We will solve it further to get: (4 – 3) (4 – 4) ?=? 0 Which will further be: (1) (0)? =? 0 and 0=0. Here LHS = RHS and hence proved correct. The example mentioned above would have surely helped you in solving quadratic equations very easily by factoring method.
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