If is the only real root of x 3 + bx 2 + cx + 1 = 0 (b< c)…

Maths Differentiation and Applications of Derivatives NTA Abhiyas Question - Applications of Derivativas Subjective Type

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If is the only real root of x 3 + bx 2 + cx + 1 = 0 (b< c), then the value of | [ ] | is (where, [. ] represents the greatest integer function)

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The correct answer is:

CHECK THE SOLUTION.

Let, f(x) = x 3 +bx 2 +cx + 1

f(x) = 0 has only one real root so it is an increasing function

Now, f(0) = 1, f (-1) = -1 + b -c +1

f(-l) = 6-c<0

using mean value theorem, real root must lie between (-1,0)

so, [ ] = -1

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