Question

Polynomial function that has the zeros -5 and 4i

Answer 1

Answer:

$P(x) = x^{2} + x(5-4i) - 20i$ is the required polynomial function of the form $ax^{2} + bx +c$

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, $P(x) = x (x-4i) + 5(x-4i) = x^{2} - 4ix + 5x - 20i$

⇒$P(x) = x^{2} + x(5-4i) - 20i$

Hence, P(x) is the required polynomial function of the form $ax^{2} + bx +c$