Answer:
[tex]P(x) = x^{2} + x(5-4i) - 20i[/tex] is the required polynomial function of the form [tex]ax^{2} + bx +c[/tex]
Step-by-step explanation:
The given zeroes of the polynomial is -5 and 4i.
It implies, the roots of the polynomial is (x+5) and (x-4i)
Now, The Polynomial = Product of all its roots
So, here P(x) = ( x + 5)( x - 4i)
or, [tex]P(x) = x (x-4i) + 5(x-4i) = x^{2} - 4ix + 5x - 20i[/tex]
⇒[tex]P(x) = x^{2} + x(5-4i) - 20i[/tex]
Hence, P(x) is the required polynomial function of the form [tex]ax^{2} + bx +c[/tex]
