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State whether the given statement is true or false.

We can write a polynomial function with the given zeros 2 ,2i and degree 3

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True

False

answer is A.

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Detailed Solution

The given statement is true.
Concept- We use the factor theorem to conclude that if

are the roots of a polynomial of third degree
(cubic) then the polynomial is given by

. We recall the nature of zeroes of cubic polynomials that if one zero is real then the other two will be complex conjugates. To obtain the third zero, we utilise it as

We know that complex zeros are in the form

. Here we have one complex zero

. Then the other zero is

So the third factor is

So the required degree 3 polynomial is

Hence, the given statement is true.

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