which of the following describes the roots of the polynomial function f x x 2 2 x 4 x 1

Roots of a polynomial is defined as the values of a variable(i.e x) for which the given polynomial is equal to zero. If "a" is the root of the polynomial q(x), then q(a) = 0.

We have given that,

f(x) = (x + 2)² (x - 4) (x + 1)

we have find out all roots of f(x) .

The roots of polynomial function are the values of x which gives f(x) = 0 so,

( x + 2)²(x - 4) (x + 1) = 0

product of three factors equal to zero implies that either one , two or all are equal to zero

mathematically, ( x+2)² = 0 or (x - 4) = 0 or

(x + 1)=0

Now, ( x+2)² = 0 gives x= -2 with multiplicity 2 because power of factor 2 .

similarly, (x - 4) = 0 , gives x = 4 with multiplicity 1

(x + 1) = 0 => x = -1 with multiplicity 1

So, we got all the three roots of given f(x) i.e -2, 4, -1..

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Complete question:

Which of the following describes the roots of the polynomial function f(x) = (x + 2)^2 (x - 4) (x + 1)?

a) -2 with multiplicity 2, 4 with multiplicity 1, -1 with multiplicity 1,

b)-2 with multiplicity 3, 4 with multiplicity 2, and -1 with multiplicity 1

c) 2 with multiplicity 2, -4 with multiplicity 1, and 1 with multiplicity 1

d)2 with multiplicity 3, -4 with multiplicity 2, and 1 with multiplicity 4