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Five root function (Posted on 2021-05-07) Difficulty: 3 of 5
Given that the polynomial P(x) = x5 - x2 + 1 has 5 roots r1, r2, r3, r4, r5. Find the value of the product Q(r1)Q(r2)Q(r3)Q(r4)Q(r5), where Q(x) = x2 + 1.

No Solution Yet Submitted by Danish Ahmed Khan    
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Answer. | Comment 1 of 6
Wolfram|Alpha gives the 5 roots, two pairs appear to be complex conjugates:
-.808731
-.464912 +/- 1.07147i
.869278 +/- .388269i
(It can't seem to figure out the exact forms)

This means the product sought will be a real number.  

Plugging the values into Q, my calculator shows the values 4.999973
which I would guess should actually be 5.

I don't know how to solve exactly.  
Note: the product of the 5 roots is -.999995 (probably -1)


  Posted by Jer on 2021-05-08 12:23:10
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