ANSWER
a. 2 real roots, 2 imaginary roots
EXPLANATION
The given equation is
[tex] {x}^{4} - 64 = 0[/tex]
We rewrite as difference of two squares,
[tex]( {x}^{2} )^{2} - {8}^{2} = 0[/tex]
We factor using difference of two squares to get;
[tex]( {x}^{2} - 8)( {x}^{2} + 8) = 0[/tex]
We now use the zero product property to get:
[tex]{x}^{2} = 8 \: or \: {x}^{2} = - 8[/tex]
Take the square root of both sides to get;
[tex]{x} = \pm \sqrt{8} \: or \: {x}^{2} = \pm \sqrt{ - 8} [/tex]
[tex]{x} = \pm 2\sqrt{2} \: or \: {x} = \pm 2\sqrt{ 2} i[/tex]
[tex]{x} = - 2\sqrt{2} \: or \: {x} = 2\sqrt{ 2}[/tex]
are two real roots.
[tex]{x} = - 2\sqrt{2}i \: or \: {x} = 2\sqrt{ 2} i[/tex]
are two imaginary roots.
The correct answer is A.
