Answer:
f(x) = is the required polynomial.
Step-by-step explanation:
Given the zeroes (roots) of the polynomial are and
.
We know that complex roots occur in conjugate pairs.
So, this means that and
would also be the roots of the polynomial.
If are to be the roots of the polynomial then the polynomial should have been:
.
Now, to determine the polynomial for which would be the roots.
Roots of the polynomial are nothing but the values of x (any variable) that would make the polynomial zero.
⇒
⇒
The required polynomial would be the product of all the above polynomials.
Multiply this to get the required equation.
⇒
∴ The required polynomial is x⁴ - 2x³ + 49x² - 18x + 360 = 0.