Find a polynomial P(x)=0 in standard form with integer coefficients whose roots are 2/3, -4, 3+i sq root 5.
Can someone teach me how to start it? thank you!
Think about it this way. If you have a polynomial $\displaystyle P(x) = x^2+2x-3$ you can factor it to $\displaystyle P(x) = (x-1)(x+3)$. Is it clear that the roots are $\displaystyle x=1$ and $\displaystyle x=-3$ ?
(a root is where a function crosses the x-axis, or equivalently when P(x)=0)
If this makes sense to you, then the question that you have to answer is simply doing this procedure backwards.
In other words, $\displaystyle P(x) = (x-\frac{2}{3})(x+4)(x-(3+i\sqrt5))$