Question

Find a quadratic polynomial, the sum and the product of whose zeroes are $2$ and $-15$.

Answer 1

We know that every quadratic equation is based on this relation..

$p\left(x\right)=kx²-(\alpha +\beta )x+\alpha \beta$

where, α and β are the zeroes of given polynomial.

Now putting values of $(\alpha +\beta )=2$ and $\alpha \beta =-15$ in above equation, we get ...

$p\left(x\right)=x²-2x-15=0$