perplexus.info :: Just Math : Arithmetic Roots

Arithmetic Roots (Posted on 2016-03-02)

For what values k does the polynomial f(x) = x^4 + 7x^3 + 9x^2 - 7x + k have three roots in arithmetic progression?

Submitted by Brian Smith

Rating: 4.0000 (1 votes)

Solution: (Hide)

Harry does a good job explaining the possible values are
k = -10, (-553 – 159(-13 +/– sqrt(57))/8)/64.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Analytic solution (outline)	Harry	2016-03-02 12:19:05
solution with computer assist	Charlie	2016-03-02 10:32:09

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