The equation $a x^{2} + b x + c = 0$ will be an identity iff

a = b = c = 0

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a = b = c \neq 0

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a \neq b \neq c = 0

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Solution

The correct option is A $a = b = c = 0$
Any equation is called an identity iff the equation holds true for all values of the variable.

$∴$ For any polynomial equation $a_{n} x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{1} x_{1} + a_{0} = 0$ iff all the coefficients of the polynomial equation is equal to $0$
$\Rightarrow a_{n} = a_{n - 1} = a_{n - 2} = \dots = a_{1} = a_{0}$

Thus, for our equation to be identity:
$a = b = c = 0$

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The equation ax2+bx+c=0 will be an identity iff

The equation $a x^{2} + b x + c = 0$ will be an identity iff