If 1,2,3,4 are the roots of the equation x4+ax3+bx2+cx+d=0, then ‌‌(x−1)(x−2)(x−3)(x−4) =x4+ax3+bx2+cx+d ⇒‌‌(x2−3x+2)(x2−7x+12) =x4+ax3+bx2+cx+d ⇒‌‌x4−10x3+35x2−50x+24 =x4+ax3+bx2+cx+d ⇒‌‌a=−10,b=35,c=−50,d=24 ‌ Now, ‌‌‌a+2b+c=−10+2×35−50 =10