Question

Which of the following describes the roots of the polynomial function f(x)=(x+2)^2(x-4)(x+1)^3

Answer 1

Answer:
Roots of given polynomial function are real ,and repeated,these are

-2,-2,4,-1,-1,-1


Step by step solution:

To find the roots of given polynomial function f(x) we must equate it to zero

$f(x) = 0 \\ \\ {(x + 2)}^{2} (x - 4)( {x + 1)}^{3} = 0 \\ \\ {(x + 2)}^{2} = 0 \\ \\ x = - 2 \\ \\ x - 4 = 0 \\ \\ x = 4 \\ \\ {(x + 1)}^{3} = 0 \\ \\ x = - 1$
Thus this polynomial has 6 roots and two are repeated
-2,-2,4,-1,-1,-1