The number of integral values of k for which x 2 − 2 ( 4 k − 1 ) x + 15 k 2 − 2 k − 7 ≥ 0 hold for all x is

D < 0 ⇒ k 2 − 6 k + 8 < 0 ⇒ 2 ≤ k ≤ 4 ⇒ k = 2 , 3 , 4 ⇒ 3 values

Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationInequationEasy2 minQB

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The number of integral values of $k$ for which $x^{2} - 2 (4 k - 1) x + 15 k^{2} - 2 k - 7 \geq 0$ hold for all $x$ is

Answer:

Solution:

$D < 0 \Rightarrow k^{2} - 6 k + 8 < 0 \Rightarrow 2 \leq k \leq 4$

$\Rightarrow k = 2, 3, 4 \Rightarrow 3$ values

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Inequation

⏱ 2mℹ️ Source: QB

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