[tex]\displaystyle\bf\\x^{4} +5x^{2} +4=0\\\\x^{2} =m \ , \ m > 0\\\\m^{2} +5m+4=0\\\\D=5^{2} -4\cdot 4=25-16=9=3^{2} \\\\\\m_{1} =\frac{-5+3}{2} =-1 \ < 0 \ ne \ podxodit\\\\\\m_{2} =\frac{-5-3}{2} =-4 \ < 0 \ ne \ podxodit[/tex]

Ответ :  корней нет