Applications of Quadratic Equations

The present concept is dealing with the aspect of Quadratic Equation and its application. This equation is generally used in the time of multiplication of two things. The important factor of this field is that two of the things are dependent on the same variable. It is an important topic of mathematics and the readers can get the solutions from this part. The readers can get a clear idea about its application, formula, and example throughout the entire study and different matters related to it.    

What Is Meant By Quadratic Equations?

It is an equation that has one term and in that term, the unknown is squared. It is also important in that part that it cannot be raised to a higher power. This equation is also known as a polynomial equation. Different methods can be applied for the solution to this equation. The majority say that there are four major methods for the solution to this equation. They can be the use of square roots, use of quadratic formula, use of factors, and completion of the square. Its use can be seen in situations where the use of two things and their multiplication depend on the same variable. This is the most important part of this study that describes the aspects related to it.      

Application of Quadratic Equations

In this field, it can be seen that many problems related to mathematics and physics are in the form of quadratic equations. Both the fields of physics and mathematics have the importance of this equation. In the mathematical field, the importance of this equation is notable. The important factor of this equation is that when D < 0, then the equation has no solution. The vast field of mathematics has its own application of this formula. The important factor of this equation is that it can be seen in many forms.   

Solving the Quadratic Equation

This is the expression that means the algebraic expression of second-degree. This is the part of the study that means the important part and it denotes the matter of description in a different way. A formula is needed for the solution of this expression and it says that ax2+bx+c=0. In this aspect b and a are the coefficients, c is the constant term, and x is the variable here. 

Quadratic Equations and Motion Problem

•  An object has launched from the ground in a 39.2m/s upward direction. How will the object stay at a height of 34.3m?

The equation will be:

s(t)=-4.9t2+39.2t

-4.9t2+39.2t=34.3

t2-8t+7=0

(t-7)(t-1)= 0 

Discussion on Quadratic Formula

Discussing the formula can be mentioned that it is the simplest way of finding a quadratic equation. A certain quadratic equation can be seen that cannot be easily factored in. It is an expression of algebra and has its own formula. 

The formula says: ax2+bx+c=0

In this place ‘x’ is considered to be the variable, ‘b’ and ‘a’, here indicate coefficient, and ‘c’ means the constant term. The first condition for an equation that is quadratic is the coefficient of ‘x2‘. It is a term that indicates a non-zero expression such as a not equal to zero. In the time of writing a quadratic equation in its standard form, ‘x2’ is written first.       

Example of This Process

• Example: A ball has flipped upward from the top of a roof, and it is 80m above the ground. The ball will reach the maximum height and then fall down. The ball’s height is ‘h’ at the time ’t’ and it is given by ‘h’ = -16t 2+64t+80. Then find the height of the ball after 1 second, and the maximum height that the ball reached.

For finding the height of the ball after 1 second, it is:

-16(1) 2+64(1) +80 = 128

Finding the maximum height of the ball the equation will be:

-16[t 2-4t-5] = -16[(t-2)2-9] = -16(t-2)2+144

Conclusion 

This is the factor of the study that describes the quadratic equation and its application. It is an important part of mathematics and it deals with its application in various fields. The study enriched the discussion of the equation’s application. The meaning of the study is very clear here and they provide the solution in various ways also. The important part here is that the application of this equation is not only seen in the field of mathematics but also it is a matter of description in the field of physics.