The first step to solving the problem is to expand the polynomial to determine the number of roots.
The polynomial
(x+7)(x-2)²(x²-4)(x+1)⁴
Can be expanded as
x⁹ + 7 x⁸ - 10 x⁷ - 74 x⁶ + 5 x⁵ + 259 x⁴ + 164 x³ - 272 x² - 352 x - 112
The real number roots will be the following
x= -7
x= -2
x= -1
x= 2
