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From the root of cubic polynomial (Posted on 2023-09-16) Difficulty: 4 of 5
Let P(x) be a polynomial with degree 3, consider the polynomial

Q(x)=(x3-2x+1-P(x))(2x3-5x2+4-P(x)).

Assume that Q(x)≤0, ∀x and P(0)=3. Calculate Q(-1).

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(3): Solution Comment 4 of 4 |
(In reply to re(2): Solution by Larry)

I was suspicious because the difference was a cubic, and a cubic has 1 or 3 real roots.  Of course, if it has 3 real roots, then 2 or 3 of them can be identical, so I had to check to see if the 3 real roots were distinct, which they were.
  Posted by Steve Herman on 2023-09-17 06:31:56

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