If the expression (x^2-11 x+a ) and (x^2-14 x+2 a ) must have a common factor and ( a 0 ), then, the common factor is

Step-by-step solution

Here Let (x- ) is the common factor then ( x = ) is root of the corresponding equation ( ^2-11 +a=0 ) ( ^2-14 +2 a =0 ) Subtracting (3 -a=0 =a / 3 ) Hence ( a^2 9 -11 a 3 +a=0, a=0 ) or (a=24 ) since ( a 0, a =24 ) ( ) the common factor of ( array l x^2-11 x+24 x^2-14 x+48 array . ) is clearly (x -8 )