System of second degree equations in 2 variables

Sage Fry

Sage Fry

Answered question

2022-04-03

System of second degree equations in 2 variables
{ax22x+y22=03x2+x2y+2=0
I need to find all aR for which the system above has 2 real solutions. The problem also asks me to solve the system for a=1. It looks like the system has 2 real solutions and 2 complex solutions for a=1.

Answer & Explanation

Deon Frost

Deon Frost

Beginner2022-04-04Added 6 answers

Write y=12(3x2+x+2) by the second equation. Then the first equation is
4ax2+9x46x311x24x4=0
For a=1 this equation has two complex solutions and two real solutions - as you said. In general, for a polynomial, we can use the rule of Descartes and others.

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