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Question
Solve `x^2+5x-(a^2+a-6)=0`
Solution
`x^2+5x-(a^2+a-6)=0`
⇒`x^2+5x-(a+3)(a-2)=0`
⇒`x^2+[(a+3)-(a-2)]x-(a+3)(a-2)=0`
⇒`x^2+(a+3)x(a-2)x-(a+3)(a-2)=0`
⇒`x[x+(x+3)]-(a-2) [x+(a+3)]=0`
⇒`[x+(a+3)] [x-(a-2)]=0`
⇒`x+(a+3)=0 or 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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