Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

Question

3 years ago

10

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

tandard form.
7, -11, and 2 + 6i

f(x) = x4 - 53x2 + 468x - 3080

f(x) = x4 - 9x3 - 42x2 + 234x - 3080

f(x) = x4 - 117x2 + 468x - 3080

f(x) = x4 - 9x3 + 42x2 - 234x + 3080

Mathematics

1 answer:

r-ruslan [8.4K] · Answer 1 · 2022-01-26T10:19:23+03:00

The first thing you should do is to determine all the zeros, and you will have 7, -11, 2 + 6i, 2 - 6i.
After that you have to subtract and (x) from every each zero that you have above, which means
 $7-x, 

 -11-x, 

2 + 6i-x,

 2 - 6i-x
$
And the last step is to multiply them together, and that's all you need!
 $(7-x)(-11-x)(2 + 6i-x)(2 - 6i-x)$
I am pretty sure that everything hase become clear! Regards.