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Discriminant

The least int...

Question

The least integral value of k such that $(k - 2) x^{2} + 8 x + k + 4$ is positive for all real values of x is

A

1

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B

2

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C

3

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D

5

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Solution

The correct option is D 5
$(k - 2) x^{2} + 8 x + (k + 4) > 0 \forall x \in R$
$D = 64 - 4 (k - 2) (k + 4) < 0$ and $k - 2 > 0$
$(k + 6) (k - 4) > 0 k > 2$
$k < - 6 o r k > 4$
$k > 4$
$k = 5$

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