Question

find the no. of polynomials whose zeroes are -2 & 5​

Answer 1

Beta are zeroes of the polynomial

$\sf p(x) = {x}^{2} - (\alpha + \beta )x + \alpha \beta(x)$

Therefore the polynomial is

$\begin{gathered}\sf Let \: \alpha = 5 \: and \: \beta = - 2 \\\sf \alpha + \beta = 5 - 2 \\ = 3 \\ \sf\\alpha \beta = 5 \times - 2 \\\ = - 10\end{gathered}$

$\sf (x) = {x}^{2} - 3x - 10p(x)=x −3x−10$

✰$\sf HENCE\: FOUND$✰