Respuesta :
Given
The equation in the form
[tex]x^{4}+95x^{2}-500 =0[/tex]
Find the factor of the above equation
To proof
factoring the above equation
we get
[tex]x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0[/tex]
now sloving the equation we get the value
x² = 5
x² = -100
[tex]x =\pm \sqrt{5}\\\\ x=\sqrt{-100}[/tex]
The factor of the equation is
[tex]x=\pm \sqrt{5}\\\\ x= \pm 10i[/tex]
Hence proved
