Question 309511
Use a substitution, {{{u=w^2}}}, then {{{u^2=w^4}}}
{{{w^4-4w^2-2=0}}}
{{{u^2-4u-2=0}}}
Complete the square.
{{{u^2-4u+4-2=4}}}
{{{(u-2)^2-2=4}}}
{{{(u-2)^2=6}}}
{{{u-2=0 +- sqrt(6)}}}
{{{u=-2 +- sqrt(6)}}}
{{{w^2=-2+- sqrt(6)}}}
{{{w=0 +- sqrt(-2 +- sqrt(6))}}}
Two real roots, two complex roots. 
 {{{ graph( 300, 300, -3, 3, -10, 10,x^4-4x^2-2) }}}