# Thread: need help with polyonomial in standard form

1. ## need help with polyonomial in standard form

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!

2. Originally Posted by Thatoneguy12345
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 $P(x) = x^2+2x-3$ you can factor it to $P(x) = (x-1)(x+3)$. Is it clear that the roots are $x=1$ and $x=-3$ ?
(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, $P(x) = (x-\frac{2}{3})(x+4)(x-(3+i\sqrt5))$

3. Originally Posted by Thatoneguy12345
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!
$P(x) = k\left(x - \frac{2}{3}\right)(x+4)[x - (3+i\sqrt{5})][x - (3-i\sqrt{5})]$

where $k$ is the constant necessary to make integer coefficients