given f(z)=72z+144z^2-129 solve f(z)=6

Question

I cannot figure these questions out. This is one of them. Thank you.

Answer 1

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