If {x_1}, {x_2}, {x_3} are distinct roots of | vedclass

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(D) quadratic equation of the form $ax^2 + bx + c = 0$ can have at most two distinct roots unless it is an identity.If an equation has more than two d

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$a = b = c = 0$

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(D) quadratic equation of the form $ax^2 + bx + c = 0$ can have at most two distinct roots unless it is an identity.If an equation has more than two distinct roots,it must satisfy the condition that all its coefficients are zero.Therefore,for the equation to have three distinct roots ${x_1}, {x_2}, {x_3}$,it must be an identity,which implies $a = 0, b = 0,$ and $c = 0$.

If ${x_1}, {x_2}, {x_3}$ are distinct roots of the equation $ax^2 + bx + c = 0$,then:

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