Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsMedium2 minPYQ_2019

MathematicsMediumsingle choice

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

Answer:

Solution:

Let $2^{x} = t$

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

$\Rightarrow \underset{g (t)}{|t - 1|} = \underset{f (t)}{(t^{2} - 2 t - 5)}$

Since, $2^{x} > 0 \forall x \in R \Rightarrow t > 0$

From the graph, we have

It is clear from the graph that the two graphs have only one point of intersection.

So, number of real roots of the given equation is $1 .$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: PYQ_2019

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