Please help me figure this problem out someone please....
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; Zeros: 1; -i;8+i

Question

Please help me figure this problem out someone please....
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; Zeros: 1; -i;8+i

jdoe0001 · Answer

http://openstudy.com/study#/updates/51e2fb04e4b076f7da4275b5

whpalmer4 · Answer

Okay, real coefficients implies that you have complex roots in conjugate pairs: $a \pm bi$ where $i = \sqrt{-1}$.  That extends your list of zeros by 2, giving you the required 5.

Now you can form a polynomial by multiplying factors where each factor is
$(x-z_i)$ where $z_i$ is a zero of the polynomial.  You have 5 zeros, so you'll have $$f(x) = (x-z_1)(x-z_2)(x-z_3)(x-z_4)(x-z_5)$$

anonymous · Answer

that is totally wrong.... but thanks!!

whpalmer4 · Answer

What is totally wrong?

anonymous · Answer

the only thing i can really tell you bout this is that with the -i there must b a i and with the 8+i there is a 8-i so your true monomials for all this is
f(x)=(x-1)(x-i)(x+i)(x-(8+i))(x-(8-i))