##
**Quadratic
Equation**

A

**quadratic equation**is a second degree equation in a single variable. For example:*x*etc.^{2}– 25 = 0, 4x^{2}– 81 = 0, x^{2}+ 3x + 2 = 0, 2x^{2}– 7x – 15 = 0
The general form of quadratic equation

**, where***ax*^{2}+ bx + c = 0*a, b*and*c*are constants and*a ≠ 0*is called the standard form of a quadratic equation.###
**Pure
quadratic equation**

A quadratic equation of the form ax

^{2}+ c = 0, where the middle term with the variable containing power 1 is missing, is known as a**pure quadratic equation**. For example: x^{2}– 9 = 0, 2x^{2}– 5 = 0 etc. are pure quadratic equations.###
**Adfected
quadratic equation**

A quadratic equation where the second power of variable
as well as the first power of the same variable occurs is called the

**adfected quadratic equation**. For examples: x^{2}+ 9x + 14 = 0, 2x^{2}+ 5x – 3 = 0 etc. are the adfected quadratic equations.###
**Solution
of quadratic equations**

A quadratic equation is a second degree equation. So we
obtain two solutions (or roots) of the variable from a quadratic equation. In other
words, a quadratic equation has two roots. We can solve a quadratic equation by
following three methods:

*i.*

*Factorization Method*

*ii.*

*Completing the Square Method*

*iii.*

*By using formula*###
**Solving
Quadratic Equation by Factorization**

While solving quadratic equation by

**factorization method**, we factorize the second degree polynomial ax^{2}+ bx + c and expressed as the product of two linear factors. Then each linear factor is separately solved to get the required solutions of the equation by applying**zero factor property**.
In

**zero factor property**, if*p.q = 0*, then either*p = 0*or*q = 0*. In other words, if the product of two numbers is 0, then either one or both of the number must be 0.
We use the following steps to solve a quadratic
equation by the

**factorization method**.####
__Steps__:

__Steps__:

*i. Remove the brackets of fractions if there is any in the equation.*

*ii. Simplify and reduce the equation in the form of ax*^{2}+ bx + c = 0.

*iii. Factorize the left hand side into two factors.*

*iv. Use the above property of numbers and write each factor equal to 0.*

*v.*

*Solve both factors and get two values of the variable.*
The values of the variable are also called the

**roots**of the equation.
This process of

**factorization Method**will be clear by the following worked out examples.###
*Workout
Examples*

*Workout Examples*

*Example 1: Solve the following quadratic equations by factorization method:*

*a.*

*x*^{2}– 9 = 0

*b.*

*2x*^{2}= 8

*c.*

*x*^{2}– 3x – 28 = 0

*Solution:*

*a. x*^{2}– 9 = 0

*or, x*^{2}– 3^{2}= 0

*or, (x + 3)(x – 3) = 0*

*∴*

*Either, x + 3 = 0 or, x = - 3*

*Or,*

*x – 3 = 0*

*or, x = 3*

*∴*

*x = 3,*

*–3*

*b. 2x*^{2}= 8

*or, x*^{2}= 8/2

*or, x*^{2}= 4

*or, x*^{2}

*–*

*4 = 0*

*or, x*^{2}

*–*

*2*^{2}= 0

*or, (x + 2)(x – 2) = 0*

*∴*

*Either, x + 2 = 0 or, x = - 2*

*Or,*

*x – 2 = 0*

*or, x = 2*

*∴*

*x = 2,*

*–2*

*c. x*^{2}– 3x – 28 = 0

*or, x*^{2}– (7 – 4)x – 28 = 0

*or, x*^{2}– 7x + 4x – 28 = 0

*or, x(x – 7)+4(x*

*–*

*7) = 0*

*or, (x – 7)(x + 4) = 0*

*∴*

*Either, x*

*–*

*7 = 0 or, x = 7*

*Or,*

*x + 4 = 0*

*or, x =*

*–*

*4*

*∴*

*x = 7,*

*–4*

*or, 5(x*^{2}– 1) = 24x

*or, 5x*^{2}– 5 = 24x

*or, 5x*^{2}– 24x – 5 = 0

*or, 5x*^{2}– (25 – 1)x – 5 = 0

*or, 5x*^{2}– 25x + x – 5 = 0

*or, 5x(x – 5) + 1(x – 5) = 0*

*or, (x – 5)(5x + 1) = 0*

*∴*

*Either, x*

*–*

*5 = 0 or, x = 5*

*Or, 5*

*x + 1 = 0 or, 5x =*

*–*

*1 or x =*

*–*

*1/5*

*∴*

*x = 5,*

*–1/5*

*You can comment your questions or problems regarding quadratic the equations and factorization method here.*

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