What conditions would make a system of two quadratic equations

Jacquelyn Sanders

Jacquelyn Sanders

Answered question

2022-01-30

What conditions would make a system of two quadratic equations have one real solution?

Answer & Explanation

terorimaox

terorimaox

Beginner2022-01-31Added 16 answers

If we have have y=f(x)and y=g(x)[1], a solution will satisfy f(x)g(x)=0, hence we need f(x)g(x) to have exactly one solution. Quadratic equations always have exactly two solutions, so either f(x)g(x) is linear, or it has a multiple root. If it's linear, it has the form y=mx+B for some m,B (I'm using a capital B to distinguish it from the b in y=ax+bx+x, which means that the a for f and g are the same, but their b are different (if their b are the same, f(x)g(x) would be constant, and so would have infinite solutions). If it has a multiple root, then it's of the form y=A(xr)2 for some A,r, which means that the q and p for f(x) and g(x) are the same.
[1] x=y2 can also be considered a quadratic equation, but I'm assuming you're dealing with equations of the form y=f(x).

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