CAT 2008 — QA Question 3
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 value of a + b + c?
Answer & solution
- A
9
- B
14
- C
13
- D
37
Cannot be determined
Solution
The roots at f(x) = 0 are 3 and −4
∴ The equation can be written as (x – 3)(x + 4) = 0
Or, x2 − x + 12 = 0
The co-efficient of x2 is 1 here, but all equations which are multiple of this equation will also have same roots.
For example,
10(x2 − x + 12) = 0 will also have same roots
∴ (a + b + c) cannot be determined uniquely.
Hence, option (e).