Question
Download Solution PDFThe number of distinct real roots of the equation x7 − 7x − 2 = 0 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Given equation is x7 - 7x - 2 = 0
x7 - 7x = 2
f(x) = x7 - 7x and y = 2
Differentiate w.r.t. x.
f'(x) = 7x6 - 7 = 7(x6 - 1) = 7(x2 - 1)(x4 + x2 + 1)
f'(x) = 0 ⇒ x = ±1
A function f(x) is strictly decreasing at [-1,1] and increasing at some points of x < -1 and x > 1.
y = 2 intersects at 3 points.
f(x) = 2 has 3 real distinct solutions.
Hence option 4 is correct
Last updated on Jul 3, 2025
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