Question

Find a quadratic polynomial each with the given numbers as the sum and products of its zeroes

respectively :

1 1,

3 2​

Answer 1

Answer:

If zeros of quadratic polynomial f(x) are know, then find required polynomial by following formula 

Let f(x)=k{x2−(zero of zeros)+x+product of zeros},where k=a real number

Let f(x) be a quadratic polynomial

Sum and product of whose zeros are 1 and 1 respectively

f(x)=k{x2−1.x+1}=k(x2−x+1)

(where k is a constant term)

Hence, required polynomial is x2−x+1