CAT 2023 Linear and Quadratic Equations Question (Hard)

Question

Let be the largest integer such that the equation has no real roots. If is a positive real number, then the least possible value of is

Accepted Answer

Since the equation above has no real roots, the discriminant of the equation should be negative. The largest integral value that k can take is 4. Now, we need to minimize where k takes the largest integral value and y is positive are both positive real numbers, therefore, their A.M is greater than e

CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

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CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

Let kkk be the largest integer such that the equation (x−1)2+2kx+11=0(x-1)^2+2 k x+11=0(x−1)2+2kx+11=0 has no real roots. If yyy is a positive real number, then the least possible value of k4y+9y\frac{k}{4 y}+9 y4yk​+9y is

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$k$