We generally observe some equation or expression in Mathematics like x+1(Linear), x²+x+1 (Quadratic), x³+x²+x+1 (Cubic) where x is a variable.

These equations may be classified according to their degree of the polynomial. First, we need to understand what is the degree of a polynomial.

Degree of a polynomial is a higher degree in any given expression represent by variables power.

# Types of Equations

If in equation or expression higher degrees is 1 so it will be

If the expression has a higher degree 2 then it will be a

In equation have a higher degree is 3 then it will be known as a

**linear equation**as shown x+1(Linear).If the expression has a higher degree 2 then it will be a

**quadratic equation**as shown x²+x+1 (Quadratic).In equation have a higher degree is 3 then it will be known as a

**cubic polynomial**as shown x³+x²+x+1 (Cubic).**QUADRATIC
EQUATION**

An equation in which the degree of a polynomial is 2 then the expression is known as a quadratic equation.

**ax²+bx+c**. where a is the coefficient of

**x²**, b is the coefficient of

**x**&

**c**is a constant term.

Examples :-

**2****x²-5x+3****, 6****x²-x-2****,****2x²+x-6****,****x²-3x-10****.****If we compare the given example & general form of Quadratic Equation so we get below results-**

**2**

**x²-5x+3**where a=2, b=-5 ,c=3

**6**

**x²-x-2**where a=6, b=-1, c=-2

**2x²+x-6**where a=2, b=1, c=-6

**x²-3x-10**where a=1, b=-3, c=-10

So how is
Quadratic Equation its variable & coefficient, I think you understand very
well.

Now we discuss how Factorisation method is used to find the
solution (roots or zeroes) of any Quadratic Equation.

**FACTORISATION
METHOD:-**

It is a method
which is used to find the value of a variable or to find the solution (roots or
zeroes) for Quadratic equation.

We do factors of terms in Quadratic equation.
Yes, a question arising...How do we factor & find its solution?

Let's
discuss with an example-

*Example:-*

*Example:-*

*Find the zeroes of quadratic equation 2x²-5x+3.*

*Solve:-*

We are taking a Quadratic equation

**2****x²****-5x****+****3**& split its middle term**-5x**. For split, it, first multiply**2**(coefficient of**x²**) &**3**(constant term).When
multiplying

**2**&**3**we get**6****(2×3=6)**.Now this

**6**taken as reference for splitting.

Now look middle term

**-5x**we need to split it.

We may split

**-5x**in different ways

**(-1x - 4x = -5x) ,(-2x - 3x = -5x), (-6x + x = -5x) etc.**

**But remember when we multiply above both numbers (shown from red text) then we should get**

**+6**, like

**(-2 × - 3 = +6)**& when we subtract or add both number then we get

**-5x**,like

**(-2x - 3x = -5x).**

**Condition satisfying by above-highlighting portion, so we use it for splitting.**

Now find
its solution (roots or zeroes) & take equal to zero -

**= 2**

**x²**

**-5x**

**+3**= 0

**=**

__2__

__x²__

__-2x__-__3x____= 0 {Now, will take common from underline terms }__

**+3****= 2x**= 0 {Taking common underline terms}

__(x-1)__- 3__(x-1)__**=**= 0 {Now, we will take underlined terms equal to zero}

__(x-1)(2x-3)__**= (x-1) = 0 , (2x-3)**= 0

**= x-1**= 0 ,

**2x-3**= 0

**= x=1 , x = 3/2**

Finally
we get our answer (roots or zeroes) **x=1 & x = 3/2** for Quadratic
Equation **2****x²-5x+3**.

You may solve other examples from this method.

In some cases factorisation method does not work so we use another method. We will discuss more method in another post.

*For any query, you may contact us & if it is helpful then please share.*