Question

Write aa polynomial function with rational coefficents so that P(x)=0 has the given roots.

1. 2,3,5
2. square root of 3, 2i

Answer 1

1
$$
P(x)=(x-2)(x-3)(x-5)
$$
Because
$$
P(2)=0\\
P(3)=0\\
P(5)=0
$$
Similarly,
$$
P(x)=(x-\sqrt{3})(x-2i)
$$

That's it!

Answer 2

Make sense?