 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  From the root of cubic polynomial (Posted on 2023-09-16) 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.) re: Solution | Comment 2 of 4 | (In reply to Solution by Larry)

Nicely done, Larry.  I believe that you have the only solution.

If
f1(x) = x^3-2x+1  and
f2(x) = 2x^3-5x^2+4,

then the functions intersect when f2(x)-f1(x) = x^3-5x^2+2x+3 = 0.  That cubic has three distinct solutions, not 2, at -0.57577, 1.18728 and 4.38849.  So three points of intersection, not two.  and P(0) = 3 provides a 4th point that P(x) must honor, so P(x) is uniquely determined

Edited on September 16, 2023, 9:15 pm
 Posted by Steve Herman on 2023-09-16 21:02:10 Please log in:

 Search: Search body:
Forums (0)