Question

18. What is the multiple zero and multiplicity of f(x) = (x - 1)(x - 1)(x + 7)?multiple zero = 2; multiplicity = 1multiple zero = 2; multiplicity = -1multiple zero = -1; multiplicity = 2multiple zero = 1; multiplicity = 2

Answer 1

A polynomial written in factorized form is giving us the information we need about the roots or zeros.

In this case, the polynomial is:

$f(x)=(x-1)(x-1)(x+7)=(x-1)^2(x+7)$

In this case, we have two zeros: x=1 and x=-7.

NOTE: a zero "a" will be expressed in a factor (x-a). That is why the zeros are 1 and -7.

As x=1 appears 2 times as a factor, we can group the factor.

x=1 is a zero with multiplicity of 2.

Answer: the multiple zero is x=1 and has a multiplicity of 2.

multiple zero = 1; multiplicity = 2 [Fourth option]