Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. i, 2 - √3

Answer 1

Expand
\[
(x-i) (x+i)
\left(x-\left(2-\sqrt{3}\right)\right)
\left(x-\left(\sqrt{3}+2\right)\right)
\]

Answer 2

would that be the answer?

Answer 3

That is the answer
\[
(x-i) (x+i)
\left(x-\left(2-\sqrt{3}\right)\right)
\left(x-\left(\sqrt{3}+2\right)\right)=\\
\left(x^2+1\right) \left(x^2-4
x+1\right)=\\x^4-4 x^3+2 x^2-4 x+1
\]

Answer 4

If a + ib is a root, then a - ib is also a root.
If 2- \sqrt(3) is arootthen 2-\sqrt(3) is a root.

Answer 5

thank you so much would you know how to do it when it gives 1, 4, 1 + √2

Answer 6

\[(x-1)(x-4)( x -(1 +\sqrt 2)) ( x -(1-\sqrt 2))

\]

Answer 7

thank you so very much

Answer 8

yw