How do you find all zeros with multiplicities of $f(x)=x^4+2x^2-15$ ?

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Answer 1 · 2017-02-21T10:50:41

$x=+-sqrt5 i and +-sqrt 3$

$f(x) = x^4+2x^2-15$

Let say $x^2=y$
Therefore,

$(x^2)^2+2(x^2) - 15 =0$

$y^2+2y-15=0$

$(y+5)(y-3)=0$

$y = -5 and y =3$

when y =-5, then
$x^2 = -5 =5i^2$ , where $i^2 = -1$
$x=+-sqrt5 i$

when y =3, then
$x^2 = 3$ ,
$x = +-sqrt3$

How do you find all zeros with multiplicities of f(x)=x^4+2x^2-15f(x)=x^4+2x^2-15?