Question

Find a quadratic polynomial for which the sum of zero is $4$ and product is zero is $1$.

Answer 1

$\Rightarrow$ Let $\alpha$ and $\beta$ are zeros of required quadratic polynomial.

$\Rightarrow$ $\alpha +\beta =4$ ---- ( 1 ) [ given ]

$\Rightarrow$ $\alpha \beta =1$ ----- ( 2 ) [ Given ]

The required polynomial,

$x^2-(\alpha +\beta )x+\left(\alpha \beta \right)=0$

Now, using ( 1 ) and ( 2 )

$\Rightarrow$ $x^2-4x+1=0$