If  α,β  are the roots of  ax2+ bx+ c =0  then the equation whose roots α+1β , β+1α  is

The given equation is ax2+ bx+ c =0  Given roots of equation are α,β Then sum of the roots α+β=−ba Product of the roots αβ=ca If the roots are α+1β , β+1α , thenSum of the roots=α+1β+β+1α=α+β+α+βαβ                                                                =−ba−bc       (∵α+β=−ba, αβ=ca)                                                                =−b(a+c)ac Product of the roots = αβ+1+1+1αβ                                        =(c+a)2ac General quadratic equation is x2−(a+b)x+ab=0    (a,b  are roots )Required equation is x2−(−b(a+c)ac)x+(c+a)2ac=0 ⇒ acx2+b(a+c)x+(c+a)2=0