Learn and Use Quadratic Formula with an Example

Mathematics is quite tricky but an interesting subject.  It is full of equations and calculations that have much significant importance in different fields. Learning this subject is very useful to excel in various fields and also to clear many competitive exams.  So, today we will learn about a simple yet useful topic that is quadratic equations. To solve any quadratic equation you need to know its formula and steps to use the quadratic formula. In this article, you will get the introduction of quadratic equations along with its different forms and examples.

Quadratic Equation

Quadratic equation – its introduction

It is a second-degree equation that means it has at least one term with a square. The equation is always defined in its standard form. The standard form of this equation is ax² + box +c = 0 where a, b and c are the constants or coefficients. In this equation, there is a variable that is ‘X’ with an unknown value. Rest of the coefficients has known value. Using the quadratic formula, we usually find the value of this unknown variable. An equation is called quadratic if:

·         Its first variable that is ‘a’ is not equal to zero while the other variables can be zero.

·         The third variable is constant or an absolute term.

·         It must be a second-degree equation.

·         Value of unknown variable, i.e., x must satisfy the equation and hence called the root of an equation.

To understand what the quadratic equation is, here are examples of quadratic equation in its different form.

·         Standard form equation: 3x2+4x-12=0

·         Equation without the linear coefficient: x²-8=0

·         Equation without constant: 2x2+ 16x=0

·         Equation in factor form: (x+2) (x-4) =0

·         In another form: x(x-2) = 8, on multiplying and moving eight the equation comes in standard form and becomes x²-2x-8=0

These were some of the examples of quadratic equation in its different forms. Let’s see the procedure to solve these equations. Using a quadratic formula you can solve any quadratic equation, you can also use the other method where equate the factor to zero and get the value. But this method does not work for every problem as sometimes it can be quite messy because it does not get factored. The formula for the standard equation is:

                                                                     x= (-b±√ (b²-4ac))/2a

To use this formula, first, arrange the equation in the standard form.  Remember that the coefficient b will get squared completely means along with the sign. On solving the problem, you will get two roots, one with a positive value and other with the negative value. Take an example to understand the formula.

For example:

To solve x²+2x-4=0 , You can find the factor or simply put the values of a, b and c in the above formula to get the answer. Let’s solve using the quadratic formula.  The value of coefficients a, band c is 1, 2 and-4 respectively. Put them in the formula.

x= (-2±√ (2²-4.1.-4))/2.1

= (-2±√(4 +16))/2

= (-2±√20)/2

= (-2±2√5)/2   

The two roots of equation are -2+2√5/2 and -2-2√5/2

If you understand this example, then try solving other problem as well. Go with the simple problems and then move toward the tough questions. I hope you understand how to use the quadratic formula.