Question

find the quadratic polynomial whose sum and product of the zeros are-2, √3​

Answer 1

Step-by-step explanation:

$\blue{\mathfrak{\underline{\large{Sum \: of \: zeroes}}}:} \\ \alpha + \beta = - 2 - (i) \\ \alpha \beta = \sqrt{3} - (ii) \\ \blue{\mathfrak{\underline{\large{Solving \: equation \: (i)}}}:} \\ \alpha = - 2 - \beta \: \: or \: \: \beta = - 2 - \alpha \\ \blue{\mathfrak{\underline{\large{Put \: the \: value \: of \: \alpha \: or \: \beta }}}:} \\ ( - 2 - \beta ) \beta = \sqrt{3} \: \: | \: \: \alpha ( - 2 - \alpha ) = \sqrt{3 } \\ - 2 \beta - { \beta }^{2} = \sqrt{3} \: \: \: \: | \: \: - 2 \alpha - { \alpha }^{2} = \sqrt{3} \\ 0 = { \beta }^{2} - 2 \beta + \sqrt{3} \: \: | \: \: 0 = { \beta }^{2} - 2 \beta + \sqrt{3} \\ \blue{\mathfrak{\rightarrow \: These \: are \: the \: resulting\: quadratic \: equations. }} \\ \\ \red{\mathfrak{\underline{\huge{hope \: it \: helps \: you }}}} \\ \green{\mathfrak{\underline{\huge{mark \: me \: brainliest}}}}$