There are different ways that you can use to solve quadratic equations; it can be through using square roots, completing the square or to use the quadratic formula. You may have learnt how to factor but what it is new with this expression is that quadratic expression may be a part of the equation so you should solve values of a variable which make an equation to be true.
For solving quadratic through factoring, there is a need to use the Zero product property. It is the property which says that when something is not obvious but when it may have been pointed out.
Zero Product Property: when two or even more things are put together and results become zero, it means that a number of these that have been multiplied may have been equal to a zero. This means that the easy way to get zero while multiplying the factors is when among the factors there is a zero.
This means when two or even more factors are being multiplied and the answer is zero, then one of such factors already equal zero. It is easy to set every factor to equal to zero and to solve resulting equation for a solution on original equation.
It is easy to draw a helpful conclusion on the factors that any of the factors may be equal at zero to make sure that the factors do equal at zero, this is the product on its own is zero. When the product of a factor is something else but not zero, then there is no way of making such claim on the values of such factors.
This is why, if it comes to solve quadratic equations through factoring, there is a need to have an equation that the quadratic expression is zero so that the attempt of solving such quadratic equation can be done by factoring.
If the exercise asks to solve and to check, they want someone to plug the answer he gets in original exercise and to get something which may work out. The same checking technique should be used in verifying the answer and in solving the exercise. The example is when someone is not sure of a factor and then solve the question at the next test, it is about plugging the answer in an original equation and to confirm that the solution may lead to the true statements.
When the equation is not the quadratic or equals to zero, it should not be solved yet. The right thing that someone should do is getting the terms on a side while the zero is found on the other side.
Are you the one who find difficulty, in solving quadratic equations or the polynomial equations? Then do not worry as in this article you will get to know and learn how to solve quadratic equation. But before you leap to solve the equation, you must know everything about algebraic equations. Students find difficulty because they do not know the exact procedure to solve the equations. This not only prevents them from getting good grades but they also lose hope, thinking they will never solve algebraic problems. So, do read the article and solve the problems in the very short span.
What is an algebraic equation?
In mathematics, an equation of formation P = Q is known as the polynomial or algebraic equation, where P&Q are polynomials. The equation may contain single or multiple variables in a given field. For example, x^2-x+1=0 is an algebraic equation with single variable and x^2-xy-2=5 is a polynomial equation with two variables. The solution of any equation depends on the value which satisfies the given equation. The values are known as the roots of the equation. You can solve the equation using the formula as where a, b and c are the coefficient of the equation.
How to solve using the quadratic equation:
Suppose the given equation is x^2+5x+6=0, this equation can be solved using the given formula
Method 1: Here, a= 1, b= 5 and c= 6. So from the quadratic equation,
This gives, x= -2& -3.
Method 2: the Second method is known as hint and trail method. Put x= -2 in the given equation x^2+5x+6=0, if the equation becomes zero on both sides, then x will be – 2.
Similarly, put x- -3 you will get the same result. You can start by putting x=0, 1, 2…….till you find the exact solution. But using the first method seems to be safer than this as the second method consumes time.
How to factor:
Example: Suppose you have given an equation as X^2+2X+ 1=0.
Solution: The given equation can be written as
X(X+1) +1. (X+1) =0
So, the common factor is X+1 for the given problem. The whole equation as (X+1)(X+1) = X^2+2X+1.
Example: Given a higher degree polynomial as 2X^5+4X^4+2X^3+2X^2
Solution: This equation can be written as 2X^3(X^2+2X) + 2X(X^2+2X), the common factor is (X^2+2X). So, the given equation can be written as (2X^3+2X) (X^2+2X).
Best algebra software:
Have you heard of the algebra software? They are specially made to solve the quadratic equation in a matter of few seconds. There is much software available in the market, and you can take advantage of it. They provide the customer resourceful calculator so as to solve the problem. This is best known because of the fact that they not only help you out in finding solution to the problem but they also help to explore your knowledge regarding the algebra. Many of the customers have already availed the benefits of it, and if you find difficulty in finding the solution, then you too can use the software.
Now you know very well how to solve the quadratic equation quadratic equation quickly.
Different types of mathematical equations you can find in which linear, as well as quadratic equations, are common. These are the part of algebraic equations. The algebra is the part or branch of mathematics, and you can find its importance in mathematics. The algebraic system of equation contains different equations. Before learning about the system of equations, you must know some basics as-
Algebraic equations: The algebraic equation is the major part of mathematics in which various unknown values, mathematical signs, and constant values used to represent any number. While solving the algebraic expressions, you can get the values of unknown. More than one solution is possible for same variable value according to the equation.
Linear equation: liner equation includes one or more than one variable, but the variable does not include any higher degree. It means the variable has a first-order degree and you can find only one value for unknown.
Ex: x + 6 = 12
In result, you will get the value of x = 6
Quadratic equation: It comes under the algebraic equation in which you can find the second order degree of a variable. In a quadratic equation, you get two results for same variable or unknown value. For example- x² + 5x + 6 = 0
In which you can find values of x = -2 and -3
Exponential equation: It is another type of algebraic equation. In the system of equation in mathematics, exponential equations place an important role. The exponential equation shows successive increasing and decreasing variables.
Along with them, you can find various algebraic equations. Solving this algebraic equation becomes difficult when you do not have adequate knowledge of equations. Then, you need to join an online tutor to get adequate knowledge of it. On the other hand, you can choose the online platform that automatically solves the algebraic equations. You can also find the software which works offline.
How does the offline platform work?
You can choose either the website or the software for algebraic equation then you can easily solve it. First, you need to download the software on your PC. You can also buy CD to install the software on your personal computer. Now, you can use your PC to solve an algebraic equation. Some important formulas are preloaded into the software. It is not an offline tutor but solves the problem due to a pre-loaded program.
The user just needs to fill the question then press on the next tab. Now, you can get step by step solution of the equation. You can either choose the direct formula method to apply different method. The major benefit of choosing the software is that you can get the answer in few seconds. You can help your kid to solve their homework. The step by step solution of particular equation helps to understand the system of equations. Now, you can understand each operation, note down each step and understand what operations were used in the solution.
The system of equations is not difficult with the right mathematical software. It is your choices either use the particular website or download the software to solve an algebraic solution.
There have been many different fields and subjects in mathematics. All these fields are equally interesting and important at their places. Algebra is one of the most interesting and important fields of mathematics. There are many rules and regulations in mathematics. This is the perfect combination of equations and calculations. Quadratic equations hold an important place in algebra. These are very easy to solve and interesting with few simple tips and tricks. There is a set of rules designed specially to solve these equations. However, you need to know them and learn properly to get better on the subject. These are some of the best parts of algebra which can be perfect for appropriate practice.
Know more about Quadratics
There are many different methods to solve these equations within few simple steps. All these methods have different steps to be followed, but all of these bring out he correct answers. Therefore you can select the best step which seems to be easy to you. These are extremely easy when undertaken with lots of practice. Here are some easy ways to solve these equations in the best way:
Solve Equations through Factoring
Factoring is one of the most common methods used for solving quadratic equations. The only thing you need is the right information and perfect knowledge. However, all this can be acquired through practice. It is the most logical use of the powers and squares of x. There are many other methods, but this one probably holds the best place among all. It is the perfect use of some unknown and univariate equations to find out the certain value. You can be the best in this method through a bit of practice.
When you are solving an equation using a method like this, there are chances that there can be two roots or solutions. However moving in the right direction, you will surely get the right solution.
Use Quadratic Formula
Using a quadratic formula to solve an equation is another effective way to get the right answer in the best manner. This is the process if combining all like terms together and bringing them to one side. This is similar to the one which is applied in factoring. However, there are many points that you need to keep in mind while using the quadratic formula. Always ensure that you determine the values of a, b, and c and substitute them. After plugging in all the variables and values, you may carry out the necessary calculations. This formula needs to be solved step by step perfectly in order to get the right answer.
Therefore like the methods mentioned above, there are much more ways of solving these equations. Therefore you can select the best ways as per your convenience. However, the practice is the best way to become perfect in solving these equations. These equations hold the most interesting place in algebra. These are the best parts an individual goes though in mathematics. Therefore you may know more and get perfect in all the methods for solving quadratic equations. You will surely enjoy working with these methods.
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