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When polynomial and trigo unite! (Posted on 2018-04-24) Difficulty: 3 of 5
Find the number of distinct real roots of f(x) = x4 - x3 sin x - x2 cos x.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution Comment 1 of 1
The graph appears to show three real solutions:



The only question might be Does it "wiggle around" near x = 0"? But x^3 and sinx both become negative on the negative-x side and positive on the positive-x side, and x^2 and cos x are also even functions.  The function goes down both to the left and the right of the y-axis and is an even function.

So there are indeed three distinct real roots.

  Posted by Charlie on 2018-04-24 12:52:29
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