When roots of \(\displaystyleх^{{2}}+рх+{q}={0}\) are reciprocal (a

Jerimiah Boone

Jerimiah Boone

Answered question

2022-03-14

When roots of х2+рх+q=0 are reciprocal (a and 1a)?

Answer & Explanation

Spakatjlb

Spakatjlb

Beginner2022-03-15Added 4 answers

Step 1
It's pretty straight forward that is the roots of such a polynomial equation are a and 1a we have (xa)(x1a)=x2axxa+1=x2(a+1a)x+1 which is x2+px+q if and only if q=1 and p=(a+1a)
The roots are a and 1a if (xa)(x+1a)=x2+(1aa)x1. q=1 and p=1aa

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