The integral values of k for which the equation (k - 12)x2 + 2(k- 12)x + 2 = 0 possess no real roots.

Clearly, D < 04(k−12)2−8(k−12)<0(k−12)2−2(k−12)<0(k−12)(k−14)<012<k<14

The integral values of k for which the equation (k - 12)x2 + 2(k- 12)x + 2 = 0 possess no real roots.

Clearly, D < 04(k−12)2−8(k−12)<0(k−12)2−2(k−12)<0(k−12)(k−14)<012<k<14

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The integral values of k for which the equation (k - 12)x² + 2(k- 12)x + 2 = 0 possess no real roots.

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2<k<18

3<k<14

-2<k<7

2<k<14

answer is D.

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Detailed Solution

Clearly, D < 0

$\begin{array}{l} 4 (k - 12)^{2} - 8 (k - 12) < 0 \\ (k - 12)^{2} - 2 (k - 12) < 0 \\ (k - 12) (k - 14) < 0 \\ 12 < k < 14 \end{array}$

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The integral values of k for which the equation (k - 12)x2 + 2(k- 12)x + 2 = 0 possess no real roots.

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The integral values of k for which the equation (k - 12)x² + 2(k- 12)x + 2 = 0 possess no real roots.