Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively: 1,1

Answer 1

If zeros of quadratic polynomial $f\left(x\right)$ are know, then find required polynomial by following formula
Let $f\left(x\right)=k\{x^2-(zeroofzeros)+x+productofzeros\},$ where $k=a$ real number
Let $f\left(x\right)$ be a quadratic polynomial
Sum and product of whose zeros are $1$ and $1$ respectively
$f\left(x\right)=k\{x^2-1.x+1\}=k(x^2-x+1)$
(where $k$ is a constant term)
Hence, required polynomial is $x^2-x+1$