Question

How many polynomials are there having 3 and -5 as zeroes?

Answer 1

Answer:

one / infinite

Step-by-step explanation:

How many polynomials are there having 3 and -5 as zeroes?

f(x) = (x-3)(x - (-5))  Having 3 & - 5 as zeroes

=> f(x) = (x-3)(x + 5)

=> f(x) = x² + 2x - 15

Polynomial = f(x) = x² + 2x - 15

Multiplying by k

kx² + 2kx - 15k

Polynomial given above have 3 & -5 as zeroes

Putting different value of k we can get infinite Polynomial which on dividing by k will result into a unique polynomial x² + 2x - 15

If there can be additional zeroes of polynomial other than 3 & - 5

then again infinite polynomial

(x - α)(x-β).(x² + 2x - 15)  and so on