Answer and Step-by-step explanation:
Since it is a degree 3 polynomial, then it should have 3 solutions. But only one is given -7i which is an imaginary number. Since -7i is part of the solutions, then definitely, +7i is also part of the solutions. Since we are not given the last root, I would choose a suitable number in order to explain the process. Let us choose 1. Therefore, our roots are now:
±7i and 1.
In order to find the polynomial, we have:
x = +7i or –7i or 1, this means:
f(x) = (x – 7i)(x + 7i)(x – 1)
f(x) = [x² +7ix – 7ix – (7i)²](x – 1) = [x² – 49(–1)](x – 1) = (x² + 49)(x – 1) = x³ – x² + 49x – 49
