Find ALL roots of the following. Type answers in exact form, no decimals.

Question

Find ALL roots of the following. Type answers in exact form, no decimals.

x=

a=

b=

c=

d=

Answer 1

27x^3 + 64

factor using the formula

a^3 + b^3 = (a+b)(a^2-ab + b^2) where a=3x and b = 4

27x^3 + 64 = (3x+4)(9x^-12x+ 16)

set each factor = 0 and solve for x

x = -4/3 and

9x^2 -12x +16 = 0

x = 12/18 + or - (1/18)sqr(144-4(9)(16))

that gives 2 imaginary solutions