given f(z)=72z+144z^2-129 solve f(z)=6
Since f(z) = 72z + 144z^2 – 129
and f(z) = 6,
Then we can equate the two expressions for f(z), i.e.
72z + 144z^2 – 129 = 6
Rearranging and simplifying,
144z^2 + 72z – 135 = 0 (now divide by 9)
16z^2 + 8z – 15 = 0
This factorises as,
(4z – 3)(4z + 5) = 0
z = ¾, z = -5/4
The solutions are: z = 3/4, z = -5/4