Question

Find a quadratic polynomial , the sum and product of whose zeros are $-3$ $2$, respectively.

Answer 1

If zeros of quadratic polynomial $f\left(x\right)$ are know, then find required polynomial by following formula
Let $f\left(x\right)=k\{x^2-(sumofzeros)+x+productofzeros\},$

where $k=a$ real number
Let $f\left(x\right)$ be a polynomial
Sum and product of whose zeros are $-3$ and $2$ respectively
$f\left(x\right)=k[x^2-(-3)x+2]=k[x^2+3x+2](\because k=realnumber)$
Thus required polynomial $f\left(x\right)=x^2+3x+2$