Latest CAT Aptitude Question SOLUTION: Let f( x ) = ax^2 + bx + c, where a , b and c are certain constants and (a can't be 0). It is known that f(5) = -3f(2) and that 3 is a root of f(x) = 0. 1. Wh

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Let f( x ) = ax^2 + bx + c, where a , b and c are certain constants and (a can't be 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

Asked In CAT mandeep (10 years ago)

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Read Solution (4) :

Abhinav Mathur  (10 years ago)

by f(5)=-3f(2)
37a+11b+4c=0
by f(3)
9a+3b+c=0
multiply second equ. with 4 and subtract it from first
we will get a=b
now let z bt the other root of the equ.
therefore (x-3)(x-z)=ax^2+bx+c
x^2-(z+3)x+3z=ax^2+bx+c
a=1
c=3z
a=b=1
b=-(z+3)
1=-(z+3)
z=-4 (solution of first part)

now we have an equ by (x-3)(x+4)
x^2+x-12
here a=1 is a case
actual equation is ax^2+bx+c
where b=a
c=-12a
both prooved in first part
therefore equation is
ax^2+ax-12a=0
so a+b+c=a+a-12a=-10a
therefore cannot be determined

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shiv kumar garg  (10 years ago)

by the f(5)=-3f(2);
37a+11b+4c=0;
and
by f(3)=9a+3b+c=0
so by multiplying eq2 by 4 andsubtracting from eq 1 then a=b;
and by the add and multi. of root we can solve other root is -4

Is this solution Helpfull? Yes (2) | No (1)  

vanshika  (10 years ago)

this cant be solved because here we can get only two equations that are
9a+3b+c=0 ( 3 is a root)and
25a+5b+c= -3(4a+2b+c)
37a+11b+4c=0
we need to have three equation to solve this
hance it can not be solved

Is this solution Helpfull? Yes (1) | No (2)  

Ankit Lal  (10 years ago)

f(5) = −3f(2)
=> 25a+5b+c = -3(4a+2b+c) => 37a+11b+4c = 0 ---(1)
3 is a root of f(x)
=> 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
=>(x-3)(x+4) = 0 => x = 3 (or) -4

With conditions (1) and (2), it is not possible to find the value of a+b+c

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