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Question Number 122715 by ZiYangLee last updated on 19/Nov/20

	Answered by liberty last updated on 19/Nov/20

	$(a) p u t D i s c r i m i n a n t < 0 a n d α^{2} > 0$ $\Rightarrow 4 {(2 α - 5)}^{2} - 4 α^{2} . 8 < 0$ $\Rightarrow {(2 α - 5)}^{2} - 8 α^{2} < 0$ $\Rightarrow - 4 α^{2} - 20 α + 25 < 0$ $\Rightarrow 4 α^{2} + 20 α - 25 > 0$ $\Rightarrow 4 α^{2} + 20 α + 25 - 50 > 0$ $\Rightarrow {(2 α + 5)}^{2} - {(5 \sqrt{2})}^{2} > 0$ $\Rightarrow (2 α + 5 + 5 \sqrt{2}) (2 α + 5 - 5 \sqrt{2}) > 0$ $\Rightarrow α < - \frac{5 + 5 \sqrt{2}}{2} \cup α > \frac{- 5 + 5 \sqrt{2}}{2}$
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