Blanca S.
asked • 12/05/15Q: solve a polynomial
solve a polynomial with these given details.
3, zero -2 has a multiplicity of 2 and the zero 1 has a multiplicity of 3.
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1 Expert Answer
Andrew M. answered • 12/06/15
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
If a zero at a point has a multiplicity of more than 1 then the
zero at that point has a corresponding exponent: For example,
a polynomial having a zero of multiplicity 3 at x=1 will contain
the polynomial (x-1)3 ... There is a zero at x=1 and it occurs
3 times.
Since the zero at -2 has a multiplicity of 2 that means we have
(x-2)2 or (x-2)(x-2)
Since the zero at 1 has a multiplicity of 3 we have
(x-1)3 or (x-1)(x-1)(x-1)
Your polynomial is (x-2)2(x-1)3
= (x2-4x+4)(x3-3x2+3x-1)
= x5-3x4+3x3-x2-4x4+12x3-12x2+4x+4x3-12x2+12x-4
= x5-7x4+19x3-25x2+16x-4
Note that if you plug x=1 or x=-2 into this polynomial
it totals to zero.
Andrew M.
Note: I misread the original statement.
Since the zoro with multiplicity 2 is at x=-2, not x =2, the polynomial is found by:
(x+2)2(x-1)3
You can multiply that out for final answer.
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12/07/15
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Michael J.
12/05/15