Answer:
The term [tex]b^{2} - 4ac [/tex] for (x²-4x+8) and for (x²+4x+8) is negative.
Step-by-step explanation:
The x intercepts are the values of x in which the function is equal to zero. So if x⁴+64=(x²-4x+8)(x²+4x+8), the x intercepts are the values of x that satisfy:
(x²-4x+8) = 0 or (x²+4x+8) = 0
Then, the values of x that satisfy (ax²+bx+c) = 0 are calculated as:
[tex]x=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] or
[tex]x=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
So, if the term [tex]b^{2}-4ac[/tex] is negative the graph of the function has no x-intercepts.
Then, for (x²-4x+8) = 0, we get:
[tex]b^{2} - 4ac = (-4)^{2}-4(1)(8)=16-32=-16[/tex]
At the same way, for (x²+4x+8) = 0, we get:
[tex]b^{2} - 4ac = (4)^{2}-4(1)(8)=16-32=-16[/tex]
