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Question
`x^2+5x-(a^2+a-6)=0`
Solution
We write, 5x=(a+3)x-(a-2)x as
`x^2xx[-(a^2+a-6)]=-(a^2+a-6)x^2=(a+3)x xx[-(a-2)x]`
∴`x^2+5x(a^2+a-6)=0`
`⇒x^2+(a+3)x-(a-2)x-(a+3)(a-2)=0`
`⇒x[x+(a+3)]-(a-2)[x+(a+3)]=0`
⇒` [x+(a+3)][x-(a-2)=0]`
⇒`x+(a+3)=0 x-(a-2)=0`
⇒` x=-(a+3) or x=a-2`
Hence, -(a+3) and (a-2) are the roots of the given equation.
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