Concept:If (x+2) and (x−1) are factors, then x=−2 and x=1 are roots of the polynomial.Explanation:Let f(x)=2kx2+Lx+24.Since x=−2 is a root, f(−2)=0:2k(−2)2+L(−2)+24=08k−2L+24=0−2L+8k=−24...(i)Since x=1 is a root, f(1)=0:2k(1)2+L(1)+24=02k+L=−24...(ii)From equation (ii): L=−24−2k.Substitute L into equation (i):−2(−24−2k)+8k=−2448+4k+8k=−2412k=−72k=−6Now find L:L=−24−2(−6)L=−24+12L=−12Answer:L=−12 and k=−6, which is Option A.