Would an equation in the form ax+b=cx be considered quadratic?For example is 2x+3=5x quadratic?On the one hand it has two solutions, x=1 and x=−52 which is the number of solutions we'd expect from the fundamental theorem of algebra but on the other hand any equation in the form ax+b=cx would be undefined at x=0 and every quadratic equation I'm familiar with is continuous over all real numbers. Is being continuous over all real numbers necessary for an equation to be called quadratic?

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Would an equation in the form ax+b=cx be considered quadratic?For example is 2x+3=5x quadratic?On the one hand it has two solutions, x=1 and x=−52 which is the number of solutions we&#039;d expect from the fundamental theorem of algebra but on the other hand any equation in the form ax+b=cx would be undefined at x=0 and every quadratic equation I&#039;m familiar with is continuous over all real numbers. Is being continuous over all real numbers necessary for an equation to be called quadratic?

Nigel Nichols · Accepted Answer

The fact that it has two solutions is not relevant here. The equation 2x−x=0 also has two solutions, but nobody would say that it is a quadratic equation. And the equation x2+1=0 is a quadratic equation, in spite of the fact that it has no (real) solution.A reasonable definition of quadratic equation would be: an equation of the type q(x)=0, where q is a polynomial function with degree 2. It would still be a quadratic equation even if we were only interested in solutions within a certain subset of R (such as, say, (−∞,1] or Q).Under this definition, your equation is not a quadratic equation. However, its solutions are the solutions of the quadratic equation 2x2+3x−5=0.

Corbin Pittman · Accepted Answer

Ys it is quadratic because2x+3=5x ⇔2x2+3x=5⇒2z2+3x−5=0

Would an equation in the form ax+b=c/x be considered quadratic? For example is 2x+3=\fr

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