JEE PYQ: Quadratic Equation Question 39
Question 39 - 2019 (10 Apr Shift 2)
The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is:
(1) 3
(2) 2
(3) 4
(4) 1
Show Answer
Answer: (4)
Solution
Let $2^x - 1 = t$
$5 + |t| = (t+1)(t-1) = t^2 - t - 6$
When $t > 0$: $t^2 - t - 6 = 0 \Rightarrow t = 3$ or $t = -2$ (rejected)
$\therefore 2^x - 1 = 3 \Rightarrow 2^x = 4 \Rightarrow x = 2$
When $t < 0$: $r^2 + t - 6 = 0 \Rightarrow t = -3$ or $2$ (both rejected)
$\therefore$ only one solution $x = 2$
BETA
