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#