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| Math Central | Quandaries & Queries |
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Question from Susan, a student: find a polynomial function of degree three with -3 as a zero of multiplicity 2 and 4 as a zero of multiplicity 1. |
Hello Susan,
If some number 'a' is a zero of a polynomial function, then that means that (x - a) is a factor of that polynomial, and vice versa. For instance, x = 1 is a zero for the polynomial P(x) = x2 - 1, and P(x) = x2 - 1 = (x - 1)(x + 1). Also, since (x + 1) is a factor of P(x) then that implies that x = -1 is a zero of P(x).
Multiplicity is a count of how many times a root can be factored out of the polynomial. In the above example, both (x - 1) and (x + 1) have multiplicity 1. Suppose we had a polynomial that factored as Q(x) = x2(x-4). The two zeros of this polynomial are x = 0 and x = 4, which have
multiplicities 2 and 1 respectively.
Tyler
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