Two Quadratic Equations — CAT Previous-Year Questions

If the equations x² + mx + 9 = 0, x² + nx + 17 = 0 and x² + (m + n)x + 35 = 0 have a common negative root, then the value of (2m + 3n) is

Let α and β be two distinct root of the equation 2x² – 6x + k = 0, such that (α + β) and αβ are the two roots of the equation x² + px + p = 0. Then the value of 8(k - p)?

For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?

x² – y² = 0

(x – k) ² + y² = 1

If one root of x² − px + 12 = 0 is 4, while the equation x² − px + q = 0 has equal roots, then the value of q is