Question

find a quadratic polynomial with -¼,2 as sum & product of its zero respectily.​

Answer 1

Here is your solution :-

$sum \: of \: roots \: ( \alpha + \beta ) = \frac{ - 1}{4} \\ \\ product \: of \: roots \: ( \alpha \beta ) = 2$

Equation of polynomial =

${x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0 \\ \\ {x}^{2} - (\frac{ - 1}{4} )x + 2 = 0$

Multiply with 4 to remove denominator :-

$4 {x}^{2} + x + 8 = 0$

Hope it helps.