Finding all real a, b, c, d such

Aedan Berry

Aedan Berry

Answered question

2022-04-08

Finding all real a, b, c, d such that a and b are distinct roots of x2+cx+d=0, while c and d are the roots of x2+ax+b=0.

Answer & Explanation

Dallelopeelvep2yc

Dallelopeelvep2yc

Beginner2022-04-09Added 15 answers

Your system of equations approach will work here. We have 4 equations:
a+b+c=0..(1)
ab=d..(2)
a+c+d=0..(3)
cd=b..(4)
From (1) and (3), we have b=4. Substituting in (2), we get: Either b=d=0 or a=1. If the first case is true, then a,c can be any real numbers such that a+c=0 and a,c0. Otherwise, we get, from (4), c=1. So b=d=2. So one quadruplet is (a,0,a,0),a0 and the other is (1,2,1,2).

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