Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.

2(multiplicity 2), 3+i(multiplicity 1)

Question

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.

2(multiplicity 2), 3+i(multiplicity 1)

anonymous · Answer

I know that all complex numbers have a conjugate.. but this is multiplying, the other was adding.

ganeshie8 · Answer

w has multiplicity of 2, whats the factors ?

anonymous · Answer

I think (x-2)^2 (x+2)^2

ganeshie8 · Answer

*2 has multiplicity of 2, whats the factors ?

ganeshie8 · Answer

no again, real zeores font come in pairs, only complex zeroes come in pairs

ganeshie8 · Answer

*dont

anonymous · Answer

Sorry /: I was thinking complex for a second. But it is (x-2)^2

ganeshie8 · Answer

correct !

ganeshie8 · Answer

work out the complex zero

anonymous · Answer

And since complex numbers have conjugates then..

the next two zeros would be:
(x-(3+i)) and (x-(3+i)) and since multiplicity is one... there is no power.

ganeshie8 · Answer

And since complex numbers have conjugates then..

the next two zeros would be:
(x-(3+i)) and (x-(3$\color{red}{-}$i)) and since multiplicity is one... there is no power.

anonymous · Answer

Oh, simple mistake. Thanks for fixing that :P

anonymous · Answer

So now I just multiply those for standard form :)

ganeshie8 · Answer

:) you mastered these, awesome !