How do you find all the zeros of #f(x)=2x^4-2x^2-40#?

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Answer 1 · 2016-03-01T00:45:51

#x=-sqrt5,sqrt5,-2i,2i#

Set #f(x)=0#.

#2x^4-2x^2-40=0#

Divide both sides by #2#.

#x^4-x^2-20=0#

We can make this resemble a quadratic if we let #u=x^2#:

#u^2-u-20=0#

Factor to see that:

#(u-5)(u+4)=0#

So:

#u=5" "" ""or"" "" "u=-4#

Since #u=x^2#,

#x^2=5" "" ""or"" "" "x^2=-4#

These give

#x=+-sqrt5" "" "" "" "x=+-2i#