Question

Find the p(x) with a degree of 3 that has intercept in y, being y=3, 1 and i are complex zeros of this p(x). Explain step by step, please.

Answer 1

Since i is a root, -i is also a root(complex roots exist in conjugate pair). So the polynomial p(x) would be of the form a(x–1)(x–i)(x+i)

Since the y intercept is 3,

3 = a(–1)(–i)(i)

=> 3 = a(–1)

=> a = –3

So the answer is p(x) = –3(x–1)(x–i)(x+i) = –3x³ + 3x² – 3x + 3