How to Solve Quadratic Equation ? | Quadratic Equation Ko 3 Methods Se Kaise Solve Kare

How to Solve Quadratic Equation ?

QUADRATIC EQUATION ? 

    

    A quadratic equation in x is an equation that can be written in the standard form

` a x^2 + b x + c = 0 `

where a, b, and c are real numbers and a ` \neq ` 0.

    

    a represents the numerical coefficient of ` x^2 ` ,

    b represents the numerical coefficient of ` x ` , and 

    c represents the constant numerical term.

    

Example:

    ` 2 x^2 = 0 `

    ` 2 x^2 - 50 =0 `

    ` 2 x^2 - 7 x = 0 `

    ` 5 x^2 - 3 x + 3 = 0 `

    Before you solve the quadratic equation, you need to check the quadratic equation must be in standard form.

FORMULA:

    ` \ frac { - b \ pm \ sqrt { b ^ 2 - 4 a c } } { 2 a } \ `

METHODS:

There are three methods to solve quadratic equation:

    1. Quadratic formula

    2. Middle term breaking

    3. Factorization

EXAMPLE QUESTION:

    Q) `6x^2-x-2=0`

1. QUADRATIC FORMULA:

Solution:

    `6x^2-x-2=0`

    Using the quadratic formula;

    ` x =  \ frac { - b \ pm \ sqrt { b ^ 2 - 4 a c } } { 2 a } \ `

    ` x = \ frac { - ( -1 ) \ pm \ sqrt { ( -1 )^2 -4 (6) (-2) } } { 2(6) } \ `

    

    ` x = \ frac { 1 \ pm \ sqrt { ( 1 ) + ( 48 ) } } { 12 } \ `

    ` x = \ frac { 1 \ pm \ sqrt { 49 } } { 12 } \ `

    ` x = \ frac { 1 \ pm \ 7 } { 12 } \ `

                                        either            ;             or

    ` x = \ frac { 1+7 } { 12 } `                ;        ` x = \ frac { 1-7 } { 12 }`

    ` x = \ frac 8 { 12 } `                         ;        ` x = \ frac { -6 } { 12 } `

    

    ` x = \ frac 2 \ 3 `                              ;        ` x = \ frac  - 1 \ 2`

Hence,

    

    Solution Set = { ` \ frac 2 \ 3 ` , `  \ frac -1 \ 2 ` }

    

2. MIDDLE TERM BREAKING:

Solution:

3. FACTORIZATION:

 

Solution: