Let t denote the greatest integer ≤ t . Then the equation in x , x 2 + 2 x + 2 - 7 = 0 has :

x 2 + 2 x + 2 − 7 = 0 x 2 + 2 x + 2 − 7 = 0 Let x = t t 2 + 2 t − 3 = 0 t = 1 , − 3 x = - 3 , 1 x ∈ − 3 , − 2 ∪ 1 , 2 Hence, equation has infinitely many solutions.

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsMedium2 minPYQ_2020

MathematicsMediumsingle choice

Let $[t]$ denote the greatest integer $\leq t$ . Then the equation in $x, {[x]}^{2} + 2 [x + 2] - 7 = 0$ has :

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Answer:

Solution:

${[x]}^{2} + 2 [x + 2] - 7 = 0$

${[x]}^{2} + 2 ([x] + 2) - 7 = 0$

Let $[x] = t$

$t^{2} + 2 t - 3 = 0$

$t = 1, - 3$

$[x] = - 3, 1$

$x \in [- 3, - 2) \cup [1, 2)$

Hence, equation has infinitely many solutions.

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

⏱ 2mℹ️ Source: PYQ_2020

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