CAT 1995 — QA Question 26
Forming a Quadratic Equation and Relation between roots and coefficientsEasy
Passage / Data
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
One root of x2 + kx – 8 = 0 is square of the other. Then the value of k is
Answer & solution
- A
2
- B
8
- C
-8
-2
Solution
If the roots are a and a2, the product of roots = a3 = –8.
∴ a = –2.
Hence, sum of the roots = -k = (a + a2) = (–2 + 4) = 2.
∴ k = -2.
Hence, option (d).