Find all real/imaginary roots to
have you tried to solve this yourself?
try completing the square
or maybe a diff of squares
I'm stuck right after i bring the 16x over...
Where do I go from here?I have tried this, it was a test question for me today. Didn't get it so just wondering what the answer is.
HINT 1: Factor! :)
HINT 2: Think Euler!
Can someone just give the answer? I don't got a clue on how to factor it : (
No, we will not just give the answer.
Start from your equation: x^9-16x=0
What's the first thing you should look for when factoring? A common factor.
x=0,x^8=16 now solve the latter
mathelord - If he does it your way, he'll miss some roots - all of the complex ones, actually.
Meh - do as Tide suggested. Factoring is the way to go. Let me suggest you go back and review some of the basic factoring patterns - sum of cubes, difference of cubes, things of that nature.
Meh - if you've dealt with polynomial equations before, you might remember that a polynom of n-th degree has n roots (real or complex or combination of both).
So P8(x) = x8 - 16 has 8 roots.
One way of finding them is applying a very useful DeMoivre's Theorem to
x8 = 16
and extracting a root of 8th degree.
If it's not in your course, it's really worth mastering.
If you do, it will give you a serious sense of satisfaction.
Otherwise it can be done the way Tide and Diane_ suggested, except that Tide's "Euler hint" may not be needed.
Do you know how to solve
x^2 + 2 = 0 ?
x^4 + 4 = 0?
Look at the first one.
What for the second x^4 + 4=x^4+4x^2+4-4x^2;
maybe you can continue and find your answer
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