Question

the number of polynomials having zeros 2 and 1 is:​

Answer 1

infinite.............

Answer 2

Answer:

By the given polynomial will have 2 and 1 as zeros.

p(x) = (x -2)(x - 1)

But if you scale that by any non-zero constant, it will also have the same zeros.

p(x) = a(x -2)(x - 1)

So by the equation they are having infinitely many possible values of 'a', there are infinitely many polynomials.

Therefore A polynomial has  α  as a zero if and only if (x−α) is a factor of the polynomial.