## Tuesday, 15 November 2011

Directions for Questions 1 and 2:
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.
1. What is the other root of f(x) = 0?
(1)   −7        (2)   − 4         (3)     2         (4)   6        (5)   cannot be determined
2. What is the value of a + b + c?
(1)  9          (2)   14          (3)     13          (4)   37     (5)   cannot be determined
Solution follows here:
Solution:
f(x) = ax2 + bx + c
f(5) = −3f(2) => 25a+5b+c = -3(4a+2b+c) => 37a+11b+4c = 0    ---(1)
3 is a root of f(x) = 0 => f(3) = 0 => 9a+3b+c = 0                          ---(2)
On solving (1) and (2) we get, b = a, c = -12a                                ---(3)
Substituting (3) in f(x) = 0 => ax2 + ax – 12a = 0 => a(x2 + x – 12) = 0
Given that a ≠ 0 =>(x-3)(x+4) = 0 => x = 3 (or) -4
x=3 root is already given hence the other root is -4
Answer option for first question is (2)
With the given two conditions (1) and (2), it is not possible to find the value of a+b+c
Hence answer option for second question is (5)

#### 1 comment:

1. Nice Explanation