If 6 and 2 are the roots of  x2+ax+β=0  and  5,3 are the roots of x2+αx+b=0 , then the roots of the equation x2+ax+b=0  are

The given equation is x2+ax+β=0  ….. ( 1 ) 6 ,2 are the roots of Eq. ( 1 )        ⇒a=−8,β=12    (∵  x2−(6+2)x+(6×2)=0) And the given equation is x2+αx+b=0  ….. ( 2 )5,3 are the roots of Eq. ( 2 )⇒α=−8,b=15     (∵  x2−(5+3)x+(5×3)=0) ∴x2+ax+b=0⇒x2−8x+15=0        (∵  a=−8,b=15)  ⇒x2−5x−3x+15=0 ⇒(x−3)(x−5)=0 ⇒x=3,5 ∴   the roots of the equation x2+ax+b=0  are  3,5