How do i write a polynomial functions that has roots 3 and 7

Can someone check if i did this correct. it’s number 4 if you’re wondering.

Suppose that sahil knows that 45 people with ages of 18 to 29 voted. without using a calculator, he quickly says then 135 people with ages of 30to 49 voted. is he correct? how might sohil have come up with his answer so quickly?

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle