JEE Main 2021 — Application Of Derivatives Question with Solution
From: JEE Main 2021 (Online) 27th August Morning Shift
Question
The number of distinct real roots of the equation 3x4 + 4x3 12x2 + 4 = 0 is _____________.
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Show full solutionCorrect answer: 4
Correct answer
4
Step-by-step explanation
3x4 + 4x3 12x2 + 4 = 0
So, let f(x) = 3x4 + 4x3 12x2 + 4
f'(x) = 12x(x2 + x 2)
= 12x (x + 2) (x 1)
f'(x) = 12x3 + 12x2 – 24x = 12x(x + 2) (x – 1)
Points of extrema are at x = 0, –2, 1
f(0) = 4
f(–2) = –28
f(1) = –1
So, 4 Real Roots
So, let f(x) = 3x4 + 4x3 12x2 + 4
f'(x) = 12x(x2 + x 2)
= 12x (x + 2) (x 1)
f'(x) = 12x3 + 12x2 – 24x = 12x(x + 2) (x – 1)
Points of extrema are at x = 0, –2, 1
f(0) = 4
f(–2) = –28
f(1) = –1
So, 4 Real Roots
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