Two Quadratic Equations — CAT Previous-Year Questions
4 previous-year questions on Two Quadratic Equations from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Two Quadratic Equations · CAT PYQs
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)?
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
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
Answer the next 3 questions based on the information given below:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
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