Q: What is a multiplicity of zero?

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If you meant x + 5 = 4 then the multiplicity is 1.

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The discriminant of the zero polynomial, P(x) = 0, is zero because it has multiple roots at every point: For all x, P'(x) = P(x) = 0. Thus, the formula for the discriminant gives Δ = a_0^(0-2) * Π_{all different roots counting multiplicity} (one root - other root)^2 Note that the second term contains an uncountable number of zeroes multiplied together. Dividing out two of them leaves you with an uncountable number of zeroes multiplied together-- i.e. zero. The above argument can be made more rigorous by adding in all the limits and stuff.

Zero point zero zero zero zero zero zero zero zero zero zero six.

Since the question did not specify a rational polynomial, the answer is a polynomial of degree 3.

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If you meant x + 5 = 4 then the multiplicity is 1.

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