We are asked to determine a quadratic equation that has two imaginary solutions. Let's suppose that the solution of the equation is the following:
[tex]x=\pm i[/tex]This means that the two imaginary solutions are "i" and "-i". Now, we use the following:
[tex]\pm i=\sqrt[]{-1}[/tex]Substituting we get:
[tex]x=\sqrt[]{-1}[/tex]Squaring both sides:
[tex]x^2=-1[/tex]Now, we add 1 to both sides:
[tex]x^2+1=0[/tex]And thus we have obtained a quadratic equation with two imaginary solutions.
