The polynomial of degree 5, P(x)P(x) has

Answered question

2022-05-02

The polynomial of degree 5, P(x)P(x) has leading coefficient 1, has roots of multiplicity 2 at x=5x=5 and x=0x=0, and a root of multiplicity 1 at x=−5x=-5
Find a possible formula for P(x)P(x).

Answer & Explanation

star233

star233

Skilled2022-05-13Added 403 answers

Each root corresponds to a linear factor, so we can write:

P(x)=x2(x-5)2(x+5)

=x2(x210x+25)(x+5)

=x55x425x3+125x2

Any polynomial with these zeros and at least these multiplicities will be a multiple (scalar or polynomial) of this P(x)

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