perplexus.info :: Just Math : Root to Polynomial Connection

Root to Polynomial Connection (Posted on 2025-02-26)

Let 1 + √3 + √13 be a root of the polynomial x⁴ + ax³ + bx² + cx + d where a, b, c, d are integers. Find d.

No Solution Yet Submitted by Danish Ahmed Khan

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re: Guessing (spoiler?)

Comment 5 of 5 |

(In reply to Guessing (spoiler?) by Steve Herman)

Indeed,

(x-[1 + √3 + √13])(x-[1 + √3 - √13])(x-[1 - √3 + √13])(x-[1 - √3 - √13]) =

69 + 60 x - 26 x^2 - 4 x^3 + x^4

Would be interested in how you "guessed"

I am sure it involves (x-a)(x+a), but further insights would be illuminating to me. Thanks.

Posted by Steven Lord on 2025-04-24 04:35:53

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