SOLUTION: what is the multiple zero and multipicity of f(x)=x^3-14x^2+49x

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Question 316921: what is the multiple zero and multipicity of f(x)=x^3-14x^2+49x
Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3-14x%5E2%2B49x=x%28x%5E2-14x%2B49%29
f%28x%29=x%28x-7%29%5E2
Single root at x=0.
Double root at x=7.

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
what is the multiple zero and multipicity of f(x)=x^3-14x^2+49x
f(x) = x^3 - 14x^2 + 49x
we need to factor this
f(x) = x(x^2 - 14x + 49)
f(x) = x(x - 7)(x - 7)
the zeroes are 0 and 7
0 has multiplicity 1 (is a zero once)
7 has multiplicity 2 (is a zero twice)
so this function has 3 zeroes counting multiplicity