MonotonicityHard

Question

Number of roots of the equation x2 .e2-IXI = 1 is -

Options

A.2
B.4
C.6
D.infinite

Solution

     
x2 e2- x - 1 = 0
f(x) = - 1 ∀ x ≥ 0
f′(x) =
⇒ f increases in (0, 2), f decreases in (2, ∞)
Also f (0) < 0 & f(2) > 0 ⇒ Exactly one root in (0, 2)
f(x) < 0
⇒ exactly one root in (2, ∞)
⇒ exactly 2 roots in (0, ∞)
⇒ equation has exactly 4 roots
∵ f(x) is even function.

Create a free account to view solution

View Solution Free
Topic: Monotonicity·Practice all Monotonicity questions

More Monotonicity Questions

Number of solution of the equation 3tan x + x3= 2 in is...Which of the following function is not monotonic when x > 0...The function &#402;(x) = xx decrease on the interval -...The largest set of real values of x for which ln (1 + x) &#8804; x is...Consider the function f(x) = 8x2 - 7x + 5 on the interval [-6, 6]. The value of c that satisfies the conclusion of the m...