First slide

Theory of equations

Question

The roots of the equation $x^{4} - 8 x^{2} - 9 = 0$ are

Moderate

A

` $\pm 1, \pm i$
B

$\pm 3, \pm i$
C

$\pm 2, \pm i$
D

None of these

Solution

$\begin{array}{ll} ∵ x^{4} - 8 x^{2} - 9 = 0 \\ \Rightarrow x^{4} - 9 x^{2} + x^{2} - 9 = 0 \\ \Rightarrow x^{2} (x^{2} - 9) + 1 (x^{2} - 9) = 0 \\ \Rightarrow (x^{2} + 1) (x^{2} - 9) = 0 \\ \Rightarrow x = \pm i, \pm 3 \end{array}$

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