A weird equation

I have no idea how to do this,can you do me a favour?

Solve the equation $\displaystyle\large z^{6}+6z+10=0(z\in \mathbb{C})$ .

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Eisenstein's lemma.

Takahiro Waki - 3 years ago

@Takahiro Waki Oh yeah!!!! I am sorry......!! IDK why it didn't strike me before suggesting Haosen to factor the expression......!!!

Aaghaz Mahajan - 3 years ago

@Haosen Chen Lemme see........but until then, did you try factoring it into 3 quadratics, by assuming that this is reducible?? This can be done because all the roots are non real and hence occur as conjugate pairs.........It is tedious but may work.......!!

Aaghaz Mahajan - 3 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$