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An equation which is true for every value of the variable is called an identity equation.
For example,
5(a – 3) = 5a – 15, (a + b)2 = a2 + 2ab + b2
In general, any polynomial equation of n degree is an identity (satisfied by more than n values of x) then all the coefficients including constant term are zero.
Particularly if ax2 + bx + c = 0 is get satisfied by three values of x say α, β, and γ (where αβγ), then it is satisfied by all real values of x, for which a = b = c = 0.

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