Question

Consider the function f(x) = (x − 3)2(x + 2)2(x − 1).


The zero ______? has a multiplicity of 1.

The zero −2 has a multiplicity of________? .

Answer 1

we have

$f(x)=(x-3)^{2}(x+2)^{2}(x-1)$

we know that

The zero of the function is  the value of x when the value of the function is equal to zero

$f(x)=(x-3)^{2}(x+2)^{2}(x-1)$

rewrite the function

$f(x)=(x-3)(x-3)(x+2)(x+2)(x-1)$

The zero's of the function are

$x=3\ x=3\ x=-2\ x=-2\ x=1$

so

$x=3$ ------> has a multiplicity of $2$

$x=-2$ ------> has a multiplicity of $2$

$x=1$ ------> has a multiplicity of $1$

therefore

the answer is

The zero $1$ has a multiplicity of $1$

The zero $-2$ has a multiplicity of $2$

Answer 2

From the given function, f(x) = (x − 3)2(x + 2)2(x − 1);

• The zero 1 has a multiplicity of 1.
• The zero −2 has a multiplicity of 2

Zeros of a function

The function f(x) = (x − 3)²(x + 2)²(x − 1) given can be expanded so that we have;

• f(x) = (x − 3)(x-3)(x + 2)(x+2)(x − 1)

Hence, the zeros of the function f(x) are;

• x = 3, 3, -2, -2, 1

We can conclude that the zero 1 has a multiplicity of 1 and the zero -2 has a multiplicity of 2.

Read more on multiplicity of zeros;

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