How many polynomials are there whose zeroes are -2 and 5?

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More than 3

answer is D.

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Detailed Solution

It is given that the two zeroes of a polynomial are -2 and 5.
If

p (x)

be a polynomial such that

p (k) = 0,

then

x = k

is a zero of a polynomial

p (x) .

There are infinitely many polynomials, whose zeroes are -2 and 5.
Ex:

x + 2 (x − 5),

x x + 2 (x − 5),

x − 1 x + 2 (x − 5),

x 2 x + 2 (x − 5),

and so on.
Therefore there are more than 3 polynomials whose zeroes are -2 and 5.
Hence option (4) is correct.

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