Question

Is it possible to have different quadratic equations with the same solution? Explain.

Answer 1

sure if one is a multiple of the other

Answer 2

\[x^2+2x-1=0\]
\[2x^2+4x-2=0\] etc. such equations are called "equivalent"

Answer 3

That makes perfect sense! Thank you!

Answer 4

There are an infinite number of quadratics that have any given set of solutions.
geometrically if we looks at the problem
Say you have two real roots - those are the x-intercepts of the parabola. You can draw lots and lots of different parabolas that have the same x-intercepts!