Determine interval of 'a' for which the graph of quadratic expression $x^{2} + (a - 1) x + 16$ always lie above x-axis for all real $x$ .

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Solution

To lie above x-axis, descriminant must be less than 0

$\Rightarrow (a - 1)^{2} - 4.16 < 0$

$\Rightarrow (a - 1 + 64) (a - 1 - 64) < 0$

$\Rightarrow (a + 63) (a - 65) < 0$

$\Rightarrow a \in (- 63, 65)$

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