Solution:
We have to find the number of polynomials that have their zeroes as 5 and -3.The general form of a quadratic polynomial is,
where
and
are the zeroes of the polynomial. Since, the zeroes of the polynomial as 5 and -3, then,
By using the above values we get,
However, because it equals zero, we can multiply it with a constant without changing the value, i.e.,
.
where k is an infinitely variable constant.
As a result, the number of polynomials is also infinite.
Thus, there are an infinite number of polynomials with the numbers 5 and -3.
Hence, option 4 is the correct option.
