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For the given polynomial function,
f(x) = (x + 2)² (x - 4) (x + 1)
The roots of f(x) is -2 with multiplicity 2 , 4 with multiplicity 1 and -1 with multiplicity 1.
So, correct option is option(A).
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..
To learn more about Roots of polynomial function, refer:
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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