How many possible distinct roots? αx^2 +β x + γ = 0 α,β,γ ∈ R Not nearly as obvious as it seems.

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Описание к видео How many possible distinct roots? αx^2 +β x + γ = 0 α,β,γ ∈ R Not nearly as obvious as it seems.

An often overlooked/tacit condition for the Quadratic Formula to hold leads to this impossible sounding question. Even math stalwart Allison Moffett failed to note in her brief tutorial that the leading coefficient of a quadratic equation cannot be equal to zero. The reason, of course, is to avoid division by zero in the quadratic formula. If the leading coefficient is 0, all that remains is a simple linear equation to solve which is why if left un-stipulated(a≠0), there can be 3 distinct zeroes to a quadratic equation!!
This problem stumped many competition contestants!
Quadratic Equation with THREE Distinct Roots

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How many possible distinct roots? αx^2 +β x + γ = 0 α,β,γ ∈ R Not nearly as obvious as it seems.

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