"The integer 'k', for which the inequality x2 $-$ 2(3k $-$ 1)x + 8k2 $-$ 7 > 0 is valid for every x in R, is :"

"${x^2} - 2(3k - 1)x + 8{k^2} - 7 > 0$ Now, D < 0 $\\Rightarrow 4{(3k - 1)^2} - 4 \\times 1 \\times (8{k^2} - 7) < 0$ $\\Rightarrow 9{k^2} - 6k + 1 - 8{k^2} + 7 < 0$ $\\Rightarrow {k^2} - 6k + 8 < 0$ $\\Rightarrow (k - 4)(k - 2) < 0$ 2 < k < 4\n then k = 3"

Easy MCQ +4 / -1 PYQ · JEE Mains 2021

The integer 'k', for which the inequality x² $-$ 2(3k $-$ 1)x + 8k² $-$ 7 > 0 is valid for every x in R, is :

A 4
B 2
C 3 Correct answer
D 0

Solution

${x^2} - 2(3k - 1)x + 8{k^2} - 7 > 0$ Now, D < 0 $\Rightarrow 4{(3k - 1)^2} - 4 \times 1 \times (8{k^2} - 7) < 0$ $\Rightarrow 9{k^2} - 6k + 1 - 8{k^2} + 7 < 0$ $\Rightarrow {k^2} - 6k + 8 < 0$ $\Rightarrow (k - 4)(k - 2) < 0$ 2 < k < 4 then k = 3

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Subject: Mathematics · Chapter: Complex Numbers and Quadratic Equations · Topic: Complex Numbers and Argand Plane

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The integer 'k', for which the inequality x2 $-$ 2(3k $-$ 1)x + 8k2 $-$ 7 > 0 is valid for every x in R, is :

Solution

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The integer 'k', for which the inequality x² $-$ 2(3k $-$ 1)x + 8k² $-$ 7 > 0 is valid for every x in R, is :