CAT Quant Practice Problems

Question: If the roots of the equation x3 – ax2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b?
  1. \( - \frac{1}{{\sqrt 3 }}\)
  2. -1
  3. 0
  4. 1
  5. \(\frac{1}{{\sqrt 3 }}\)

Correct Option:2

b = sum of the roots taken 2 at a time.
Let the roots be n-1, n and n+1.
Therefore, $b = (n-1)n + n(n+1) + (n+1)(n-1) = n^2 - n + n^2 + n + n^2 - 1$
$b = 3n^2 - 1$. The smallest value is -1.


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