Solve the following quadratic equation for x: 4x^2 + 4bx – (a^2 – b^2) = 0 - Mathematics

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Solve the following quadratic equation for x: `4x^2 + 4bx – (a^2 – b^2) = 0`

 
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Solution

`4x^2 + 4bx −(a^2 − b^2 )= 0`

`x^2+bx-((a^2-b^2)/4)=0`

`x^2+2(b/2)x=(a^2-b^2)/4`

`x^2+2(b/2)x+(b/2)^2=(a^2-b^2)/4+(b/2)^2`

`(x+b/2)^2=a^2/4`

`x+b/2=+-a/2`

`x=-b/2+-a/2`

`x=(-b-a)/2,(-b+a)/2`

Hence, the roots are `(-b-a)/2 and (-b+a)/2 `

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2014-2015 (March) All India Set 2

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