How do you find the zeros of the polynomial function with equation #f(x)=x^3+8x^2-x-8#?
1 Answer
Mar 28, 2016
x = -8 , x = ± 1
Explanation:
The zeros are the values of x , which make the function equal zero.
ie
#x^3 + 8x^2 - x - 8 = 0 # To solve this equation for x , require to factorise it.
Consider the function 'split' into 2 pairs of terms.
hence
# [ x^3 + 8x^2 ] + [-x - 8 ]# now factor each pair
thus
# x^2(x + 8) - 1(x+8) = (x + 8)(x^2 - 1) #
# rArr (x+8)(x^2-1) = 0# solve x + 8 = 0 → x = -8
solve
# x^2 -1 = 0 → (x+1)(x-1) = 0 → x = ± 1 #
