x2−11x+a and x2−14x+2a will have a common factor, if a =
0,24
Exprssions are x2−11x+a and x2−14x+2a will have a common factor, then
⇒ x2−22a+14a=xa−2a=1−14+11
⇒ x2−8a=x−a=1−3 ⇒ x2=8a3 and x=a3
⇒ (a3)2=8a3 ⇒ a29=8a3 ⇒ a = 0, 24.
Alternate Method : We can check by putting the values of a from the options.