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:

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step-by-step explanation:

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"