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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsEasy2 minPYQ_2020

MathematicsEasysingle choice

Let $S$ , be the set of all real roots of the equation, $3^{x} (3^{x} - 1) + 2 = |3^{x} - 1| + |3^{x} - 2|$ , then

Question diagram: Let S , be the set of all real roots of the equation, 3 x 3

Options:

Answer:

Solution:

Let $3^{x} = t$
$t (t - 1) + 2 = |t - 1| + |t - 2|$
$t^{2} - t + 2 = |t - 1| + |t - 2|$

Let, $f (t) = t^{2} - t + 2 & g (t) = |t - 1| + |t - 2|$

$f (t) & g (t)$ has a solution at $t = a$ .
$3^{x} = a \Rightarrow x = \log_{3} a$ .
So, it is a singleton set.

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

⏱ 2mℹ️ Source: PYQ_2020

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