Question

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

8, -14, and 3 + 9i

Answer 1

zeroes of complex types occur in pairs so
we hv 3 + 9i and 3-9i
also 8 and -14

Answer 2

can u do it now ???

Answer 3

To do this problem, we must realize that complex roots of a polynomial with real coefficients come in conjugates, i.e. in pairs like a+bi and a-bi.
So minimally, the polynomial must have the following roots:
8, -14, 3+9i and 3-9i.

To construct such a polynomial, we would proceed in writing down the polynomial in factored form, and then expand to get the polynomial in standard form.
For example, the polynomial having -2,3, 4-i, 4+i would be written down as:
y(x)=(x+2)(x-3)(x-4+i)(x-4-i)
which expands to:
\(x^4-9x^3+19x^2+31x-102\)
NOTE: This is NOT the answer to the given question, just an example.

Answer 4

alright thank you, i was getting a tad confused with what the question was asking.

Answer 5

yw!