I need to write a polynomial that satisfies the given conditions

Question

It must be a degree 3 polynomial with integer coefficients with zeros -8i and 7/5

Answer 1

It must be a degree 3 polynomial with integer coefficients with zeros -8i and 7/5

if -8i is a zero, then +8i (it's conjugate) must also be a solution. So, tnis gives you

(x-8i)(x+8i)(x -7/5) multiply the first 2 factors

(x²-64i²)(x-7/5) =(x² + 64)(x - 7/5), but you need integer coefficients, so, change x - 7/5 to 5x - 7

this gives yoiu (x² + 64)(5x - 7). Multiply these together, and you have

5x³-7x² + 320 x -448 this is your 3rd degree polynomial