CAT 2017 Question Paper | Quants Slot 1

CAT Questions

This is a question from Quadratic equation. Questions from quadratic equations have appeared in every edition of CAT. This question asks to find the maximum value of an unknown variable for which the equation will have two distinct roots - think discriminant! Your CAT preparation is incomplete without mastering this topic. Get as much practice as you can in this topic because having a strong foundation in this topic can also help you in other topics.

Question 27 : If f₁(x) = x² + 11x + n and f₂(x) = x, then the largest positive integer n for which the equation f₁(x) = f₂(x) has two distinct real roots, is : [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Functions

Given that f₁(x) = x² + 11x + n and f₂(x) = x,
Then we have to find the largest positive integer n for which the equation f₁(x) = f₂(x) has two distinct real roots.
⟹ x² + 11x + n = x
⟹ x² + 11x – x + n = 0
⟹ x² + 10n + n = 0
The discriminant should be greater than zero, D > 0.
So, b² – 4ac > 0.
⟹ 10² – 4n > 0
⟹ 100 – 4n > 0
⟹ 25 – n > 0
⟹ n = 24
Hence if f₁(x) = x² + 11x + n and f₂(x) = x, then the largest positive integer n for which the equation
f₁(x) = f₂ (x) has two distinct real roots, is 24.

The question is "If f₁(x) = x² + 11x + n and f₂(x) = x, then the largest positive integer n for which the equation f₁(x) = f₂(x) has two distinct real roots, is : [TITA]"

Hence, the answer is 24