−x2−5‌‌=Ax(x+1)+B(x+1)+C(x2) −x2−5‌‌=(A+C)x2+(A+B)x+B A+C‌‌=−1,A+B=0,B=−5 Solving we get, A=5,B=−5,C=−6 ∴‌‌f(x)=x2−x+1‌‌∴‌‌f(K)=K2−K+1 Given, f(K)+A+B+C=1 ‌‌K2−K+1+5−5−6=1⇒K2−K−6=0 ⇒‌‌‌‌(K+2)(K−3)=0⇒K=3,−2 Largest value of K=3