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In this video, we cover the multiple roots theorem of polynomials, which basically states that if a is a root of p(x) = 0 with multiplicity 3, then a is also a root of p'(x) with multiplicity 2 and a root of p''(x) with multiplicity 1.
This then extends to factors where if (x - a)^3 is a factor of p(x), then (x - a)^2 is a factor of p'(x) and (x - a) is a factor of p''(x).
We use this theorem to find all of the roots of the equation p(x) = x^4 - 6x^3 + 12x^2 - 10x + 3 = 0
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