Question 184643
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^2 - 8x - 5=0]


Note that:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\  \times\  2 = 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5\  \times\  1 = -5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2\  \times\  -5) + (2\  \times\  1) = -10 + 2 = -8]


So this factors:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^2 - 8x - 5 = (2x + 1)(2x - 5) = 0]


Using the Zero Product Rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x + 1 = 0 \ \ \Rightarrow\ \ x = -\frac{1}{2}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x - 5 = 0 \ \ \Rightarrow\ \ x = \frac{5}{2}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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