Question

find a quadratic polynomial whose zeros are root 3 and 5 respectively

Answer 1

Let the polynomial be a function in 'x'.

Since zeros of the polynomial are 3 and 5(I.e., it has two zeros). Thus, (x-3) and (x-5) must be it's factors.

Also, we know that a quadratic polynomial has two zeros. Thereby, the polynomial we need to find must be a quadratic polynomial (a polynomial of degree 2).

Hence, the factorisation of our polynomial comprises of only two factors i.e., (x-3) and (x-5).

Therefore, the required quadratic polynomial is (x-3)(x-5).

Answer 2

If 3 and 5 are zeros of a polynomial then (x-3) and (x-5) must be it's factors.

Thus,

Equation is (x-5)(x-3)