CAT 2008 — QA Question 2
Forming a Quadratic Equation and Relation between roots and coefficientsEasy
Passage / Data
Answer the next 2 questions based on the information given below.
Let f(x) = ax2 + bx + c, where, a, b and c are certain constants and a ≠ 0. It is known that f(5) = −3f(2) and that 3 is a root of f(x) = 0.
What is the other root of f(x) = 0?
Answer & solution
- A
-7
-4
- C
2
- D
6
- E
Cannot be determined
Solution
âµ 3 is a root of f(x) = 0,
∴ 9a + 3b + c = 0 …(i)
Also,
f(5) = −3f(2)
∴ 25a + 5b + c = −3(4a + 2b + c)
∴ 37a + 11b + 4c = 0 …(ii)
On solving equations (i) and (ii), we get,
a – b = 0
∴ a = b
We know that sum of the roots of a quadratic equation (ax2 + bx + c = 0) is –b/a
∴ 3 + other root = −1
∴ Other root = −4
Hence, option (b).