Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationGraph and Sign of QuadraticEasy2 minPYQ_2021

MathematicsEasysingle choice

The integer $k,$ for which the inequality $x^{2} - 2 (3 k - 1) x + 8 k^{2} - 7 > 0$ is valid for every $x$ in $R$ is:

Answer:

Solution:

$x^{2} - 2 (3 k - 1) x + 8 k^{2} - 7 > 0$

Now, $D < 0$

$\Rightarrow 4 {(3 k - 1)}^{2} - 4 \times 1 \times (8 k^{2} - 7) < 0$

$\Rightarrow 9 k^{2} - 6 k + 1 - 8 k^{2} + 7 < 0$

$\Rightarrow k^{2} - 6 k + 8 < 0$

$\Rightarrow (k - 4) (k - 2) < 0$

$\Rightarrow k \in (2, 4)$

$\Rightarrow k = 3$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Graph and Sign of Quadratic

⏱ 2mℹ️ Source: PYQ_2021

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