The integral value of k for which x^2 - 2(4k | vedclass

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(B) For a quadratic expression $ax^2 + bx + c > 0$ to be true for all $x \in R$,the conditions are $a > 0$ and the discriminant $D < 0$.Here,$a = 1$,w

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$3$

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(B) For a quadratic expression $ax^2 + bx + c > 0$ to be true for all $x \in R$,the conditions are $a > 0$ and the discriminant $D Here,$a = 1$,which is $> 0$.The discriminant $D = b^2 - 4ac $D = [-2(4k - 1)]^2 - 4(1)(15k^2 - 2k - 7) $4(16k^2 - 8k + 1) - 4(15k^2 - 2k - 7) Dividing by $4$,we get $16k^2 - 8k + 1 - 15k^2 + 2k + 7 $k^2 - 6k + 8 $(k - 2)(k - 4) This inequality holds for $2 The only integer value of $k$ in this interval is $k = 3$.

The integral value of $k$ for which $x^2 - 2(4k - 1)x + 15k^2 - 2k - 7 > 0$ for all $x \in R$ is

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