Prashant K.

asked • 12/07/16

Polynomial related question

Consider the polynomial P(x)=(x-1)(x+2)(x-3)(x-4)(x-6)-100The equation p(x)=0 has two real and two imaginary roots How... Explain it..
The equation p(x)=0 has roots.
Please tell me the number of roots with their types (real/imaginary) and also explain how to find ?

Mark M.

How are P(x) and p(x) related?
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12/07/16

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Kenneth S. answered • 12/08/16

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Evidently p(x) [with a small p]  has three factors, two of which are linear (and which consequently lead to two Real roots), and the other factor is an IRREDUCIBLE QUADRATIC FACTOR which, when set to zero, has imaginary roots since its Discriminant will be negative.
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Prashant K.

There is no relation between them. They are just the same. 
Please explain the process to find out the roots?
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12/08/16

Kenneth S.

The student's answer to Mark M's comment (inquiry) is illogical...it cannot be that both THERE IS NO RELATION BETWEEN THEM and they are just the same are true.  He is using two different polynomial names (P and p) and has not defined the latter.  I think my answer is a good one.
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12/08/16

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