Number of real roots of equation 5 + |2^x - 1| = 2^x(2^x - 2) is

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4-2.Quadratic Equations and Inequations

hard

The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is

A

$4$

B

$3$

C

$2$

D

$1$

(JEE MAIN-2019)

Solution

Let $2^{x}=t$

$5+|t-1|=t^{2}-2 t$

$\Rightarrow|t-1|=\left(t^{2}-2 t-5\right)$

$g(t) \quad f(t)$

From the graph So, number of real root is $1.$

Standard 11

Mathematics

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