Lynn W.

asked • 10/11/17

Identify the number of solutions and the multiplicity

y=(x+6)2(x-7)

Andrew M.

Note:
This problem was posted as y = (x+6)2(x-7)
 
The "number of solutions" is infinite since there are no bounds
set on the value of x as posted.
 
I do believe this was meant to be posted as a request to find
the number of roots of f(x) and their values given
 f(x) = (x+6)2(x-7)
 
Jim J has solved that problem for you.
3 roots:  -6 with a multiplicity of 2   and  7 with multiplicity 1
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10/12/17

1 Expert Answer

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Jim J. answered • 10/11/17

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Hi Lynn,
The number of solutions will be 3 because you are multiplying 3 linear terms together:  (x + 6)(x + 6)(x - 7)
If you multiply those three terms together, then the first term will be x^3, which means the polynomial is cubic and has 3 solutions.
 
Those solutions are -6, -6, and 7.   [Set each factor equal to 0 and solve]
 
The multiplicity of -6 is 2, because -6 is a solution twice.
The mutlplicity of 7 is 1, because 7 is a solution only once.
 
Hope this helps!
JMJ
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