# How do you find all the zeros of #y=x^2-11x+30# with its multiplicities?

Write out a set of brackets like this

Which you can do by trial and error, so

Therefore the fully factorised form of the equation is

Solving for the roots or zeros of this:

Therefore,

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To find all the zeros of (y = x^2 - 11x + 30) with their multiplicities, you can factor the quadratic expression or use the quadratic formula. Factoring the expression gives (y = (x - 5)(x - 6)), which shows that the zeros are (x = 5) and (x = 6). Both zeros have a multiplicity of 1 because they are distinct.

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