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

1 Answer
reudhreghs
Apr 4, 2016

#x = 5, 6#

Explanation:

Write out a set of brackets like this

#(x + a)(x + b)#

You should find two constants, #a# and #b#, such that

#a + b = -11#
#a * b = 30#

Which you can do by trial and error, so

#a = -5#
#b = -6#

Therefore the fully factorised form of the equation is

#(x - 5)(x - 6) = 0#

Solving for the roots or zeros of this:

For the entire quadratic to equal zero, one or both of the pairs of brackets must equal #0#, so solve for each individual one and you will end up with two answers.

#x - 5 = 0 -> x = 5#
#x - 6 = 0 -> x = 6#

Therefore,

#x = 5, 6#

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