Use the fact that x⁴+64=(x²-4x+8)(x²+4x+8) to explain how you know that the graph of y=x⁴+64 has no x-intercepts. you need not find the solutions.

The term 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:

or

So, if the term is negative the graph of the function has no x-intercepts.

Then, for (x²-4x+8) = 0, we get:

At the same way, for (x²+4x+8) = 0, we get:

14

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.