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 – 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.