Question

Please check me. Solve the inequality. Write your answer in interval notation. Graph.
x^4 + 16 < 17x^2. My end behavior is up/up. my rational zero that works is x = 1. and i got (x-2)(x^2 + x - 16) and factor to (x-2)(x+4)(x-4).

Answer 1

my interval notation is f(x) < or equal to zero at [-4, infinity) U [2,4] U (4, infinity).

Answer 2

I find that you can factor that to (x-4)(x+4)(x+1)(x-1). You've got more intervals than you think. You know that the graph is even, so you know that you have two identical intervals on each side, and can actually write the intervals as [+-4,+-1].

Answer 3

I'm not sure if you're doing calculus at the moment, but I can show the work for figuring out where the graph is below the x-axis

Answer 4

i'm not doing calculus. that's WAY above my head

Answer 5

It's ok. But the previous solution is still valid. You can just plug in random values between -4 and -1, 0, and 1 and 4 to see how the graph interacts with each rational zero

Answer 6

(I'd recommend plugging in -2, 0, 2 and see where it goes). You know that you don't have any roots that have a squared term, so you know that it crosses the axis each time so if you plug in one, you can just make them alternate.

Answer 7

thank you