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Question
Solve `x^2+6x-(a^2+2a-8)=0`
Solution
`x^2+6x-(a^2+2a-8)=0`
⇒ `x^2+6x-(a+4)(a-2)=0`
⇒` x^2+[(a+4)-(a-2)]x-(a+4)(a-2)=0`
⇒`x^2+(a+4)x-(a-2)x-(a+4)(a-2)=0`
⇒`x[x+(a+4)][x-(a-2)[x+(a+4)]=0`
⇒ `[x+(a+4)][x-(a-2)]=0`
⇒`x+(a+4)=0 or x-(a-2)=0`
⇒`x=-(a+4) or x=(a-2)`
Hence, `-(a+4) and (a-2)` are the roots of the given equation.
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