Question

find a quadratic ploynomial, the sum and product of whose zeros are 0 and -root 2

Answer 1

Sum of zeroes =0
Product of zeroes =
$- \sqrt{2}$

$x {}^{2} - x (\alpha + \beta ) + \alpha \beta = 0$
$x {}^{2} - x(0) + - \sqrt{2} = 0$
[tex] ×{} ^{2}+(0)-\sqrt{2}=0