Question 1184587
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The standard form of a quadratic equation ONLY defines the form of the equation,

but  DOES  NOT  DEFINE  the values of the coefficients.



The values of the coefficients can be all multiplied by any non-zero coefficient,  leaving the equation  EQIVALENT;

THEREFORE,  the values of the coefficients in the standard form quadratic equation are defined only accurate to the common non-zero multiplier.



Therefore,  all your attempts to  "invent"  a new class of  Algebra problems are empty and make no sense.