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

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

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