Directions for Questions 1 and 2:

Let f(x) = ax

^{2}+ 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) = ax

^{2}+ 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 => ax

^{2}+ ax – 12a = 0 => a(x^{2}+ 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)**
Nice Explanation

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