Methods in Solving Quadratic Equations

The quadratic equation is an important part of an algebraic second-degree equation with one or more variables and with the highest power of two. Solving processes of these equations play a very important role to solve the problems of accelerated motion in physics. Freefall occurring in a vacuum is an example of accelerated motion and quadratic equations have to be solved in the problems based on this topic. Therefore, it is very important to know the process to solve Quadratic Equations. Thus, this study or note is going to give all the important pieces of knowledge students should know.

How to Solve Quadratic Equations

The solving process of the Quadratic equation is done through some steps and these steps are as follows.

• The first thing to be done is to keep the right side as zero only by taking all other factors on the right side.
• Take all as factors
• One has to make each factor’s value zero.
• Then all equations have to be solved
• Have to check all values of the variable by putting the values in the initial equation.

The Quadratic equation can be solved by

• Making squares
• Graphing
• Factoring
• Solve the equation with the help of Quadratic formulas.

The general form of the Quadratic equation is,

ax^2  + bxy + cy^2  + dx + ey + f = 0, where, the variables are ‘x’ and ‘y’ and the arbitraries are a, b, c, d, e, & f and a,b,c≠0 and b^2-4ac gives them about the shape of the curve. The simplest form is ax^2+bx+c=0 and can be solved by using the types of formulas to solve Quadratic equations.

Formula to Solve Quadratic Equation

The basic form of the quadratic equation can be solved by the following formula to solve the Quadratic equation.

x=(-b±√(b^2-4ac))/2a.

It can be said that if it is possible to rearrange the shape of a given equation in the simplest form of the Quadratic equation, it can be solved by putting the values on the formula to solve the Quadratic equation. The given formula can be given as in the form of ax^2  + bx + c = y. Then, it has to be rearranged to the simplest form of the Quadratic equation as shown in the following:

ax^2+ bx + c = y

ax^2+bx+(c-y)=0

Thereafter, it can be rewritten in the form of x=(-b±√(b^2-4ac))/2a and be solved by simplifying the right-hand side.

Importance of Quadratic Equation in Real Life

There are various uses of Quadratic equations in the daily life of humans in different ways. It can also be said that it is an important part of daily life. The fields related to the speed, area or profit determination, are also related to the Quadratic Equation. The application of the Quadratic equation can be direct or indirect. Some people even use the equation in their life without knowing it because it is related to that field naturally. The quadratics event is involved in the sports field as it helps to analyse the game play. It also plays a very important role in a student’s life, as it is very helpful to solve problems in mathematics, chemistry, or physics. Therefore, the use of the equations cannot be neglected by the students. It is very important to know how to solve quadratic equations because it takes place in most of the daily activities of a student’s life.

Conclusion

A Quadratic Equation can be recognised by looking at its formation.

• It has one or more variables
• The highest power of the variables is two.
• The equation can be presented in a graph
• The presentation in the graph will create a shape of “U” which is known as a parabola.
• It can be solved by a different method and after solving, it will give two results.
• All methods to solve a Quadratic Equation start by taking it in the simplest form of the quadratic equation.

Thus, it can be said that everyone should try to learn how to solve quadratic equations and use them in various sides of life.