CATAlgebra > Hard202020232323454545484848✅ Correct Option: 2Related questions:CAT 2023 Slot 2Let k be the largest integer such that the equation (x−1)2+2kx+11=0(x - 1)^2 + 2kx + 11 = 0(x−1)2+2kx+11=0 has no real roots. If y is a positive real number, then the least possible value of k/4y+9yk/4y + 9yk/4y+9y isCAT 2022 Slot 1For natural numbers xxx, yyy, and zzz, if xy+yz=19xy + yz = 19xy+yz=19 and yz+xz=51yz + xz = 51yz+xz=51, then the minimum possible value of xyzxyzxyz isCAT 2018 Slot 2Let f(x)=f(x)=f(x)= max{5x5x5x, 52−2x252-2x^252−2x2}, where xxx is any positive real number. Then the minimum possible value of f(x)f(x)f(x) is