Question 366752
{{{2x^4 - 5x^2 - 12=0}}}
{{{z = x^2}}}
{{{2z^2 - 5z - 12 = 0}}}
Use quadratic formula
{{{z = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 2}}}
{{{b = -5}}}
{{{c = -12}}}
{{{z = (-(-5) +- sqrt( (-5)^2 - 4*2*(-12) ))/(2*2) }}}
{{{z = ( 5 +- sqrt( 25 + 96 ))/4 }}}
{{{z = ( 5 +- sqrt( 121 ))/4 }}}
{{{z = (5 + 11)/4}}}
{{{z = 4}}}
and
{{{z = (5 - 11)/4}}}
{{{z = -3/2}}}
And since {{{z = x^2}}},
{{{x^2 = 4}}}
{{{x = 2}}}
{{{x = -2}}}
These are the real solutions
{{{z = -3/2}}} gives 2 imaginary solutions