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Real Root Rejection (Posted on 2024-11-28) Difficulty: 3 of 5
Show that the polynomial x8-x7+x2-x+15 has no real roots.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: One way | Comment 6 of 8 |
(In reply to One way by Kenny M)

Ah,  bitlife I see! Since the function is always positive, the curve never touches the x-axis. If you look at it on the graph, it looks like a raised "valley". The minimum at x ≈ 0.53 is like the bottom of the valley, but the bottom point is still higher than the x-axis. So the equation has no real solutions. It seems like a classic example of a positive function over the entire domain! 
  Posted by davis john on 2024-12-17 01:35:36

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