Question

The number of polynomials having zeroes as -2
and 5 is
​

Answer 1

infinite number of polynomials.

Step-by-step explanation:

The given zeros are -2 and 5.

Factor Theorem:

If 'a' is a zeros of a polynomial then (x-a) must be a factor of the polynomial.

We'll use this theorem to write the

polynomial.

Since, -2 and 5 are the zeros of the polynomial. hence, (x+2)(x-5) must be the factor.

Therefore, the polynomial is in the form

P(x) = k(x+2)(x-5), where k is any real number.

Now, for difference values of 'k', we'll get a different polynomial.

Since, there would be infinite number of 'k' hence, there must be infinite number of polynomials.