What should be the relationship between p and

Carleigh Young

Carleigh Young

Answered question

2022-03-12

What should be the relationship between p and q, so that
x4+px2+q=0
equations has four solutions which are successive members of arithmetic equation.

Answer & Explanation

rywleob8

rywleob8

Beginner2022-03-13Added 4 answers

Step 1
Ignoring the case p=q=0, the solutions to this equation will be of the form x=±α,±β (α>β>0) and the arithmetic sequence (in order) would be
α,β, β,α
By definition of an arithmetic progression,
αβ=2βα=3β
Applying Vieta’s formulas on x4+px2+q=0
α2+β2=p
α2β2=q
10β2=p
3β2=q
or
qp=310

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