Find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions.

two of the zeros are 4 and 1+i
the leading coefficient is -3

Question

Find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions. 

two of the zeros are 4 and 1+i
the leading coefficient is -3

mani_jha · Answer

$$f(x)=3x ^{3}+bx ^{2}+cx+d$$
f(4)=0
f(1+i)=0
Have you tried substituting these?

anonymous · Answer

I have not.

mani_jha · Answer

Well then do so.
If you put x=4, you'll get an equation.
If you put x=1+i, you'll get another.
See if you can solve those.
First substitute and write the resulting equation.

anonymous · Answer

also, remember that complex roots come in pairs... if 1+i is a root then so is 1-i

anonymous · Answer

Thanks everyone! I figured it out!