CAT Quant Practice Problems

Question: Let f(x) = ax2 + bx + c, where a, b and c are certain constants and \(a \ne 0\) 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?
  1. –7
  2. -4
  3. 2
  4. 6
  5. cannot be determined

Correct Option:2

f(3) = 9a + 3b + c = 0 f(5) = 25a + 5b + c
f(2) = 4a + 2b + c
f(5) = -3f(2) => 25a + 5b + c = -12a -6b -3c
=> 37a + 11b + 4c = 0 --> (1)
4(9a + 3b + c) = 36a + 12b + 4c = 0 --> (2)
From (1) and (2), a - b = 0 => a = b
=> c = -12a
The equation is, therefore, $ax^2 + ax - 12a = 0 => x^2 + x - 12 = 0$
=> -4 is a root of the equation.


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