Question

polynomial from zeros (-1/2,2)​

Answer 1

Answer:

${ \large{ \pmb{ \sf{★Given... }}}}$

Zeroes of Polynomial = -1/2 , 2

${ \large{ \pmb{ \sf{★To \: Find... }}}}$

Polynomial from zeroes..?

${ \large { \pmb{ \sf{★Used \: Formula... }}}}$

${ \rm{Genera l\: Form = k \bigg[ {x }^{2} - ( \alpha + \beta )x + \alpha \beta \bigg]}}$

${ \large{ \pmb{ \sf{★ Solution... }}}}$

${ \implies{ \sf{k \bigg[ {x}^{2} - \bigg( \frac{ - 1}{2} + 2 \bigg)x + \frac{ - 1}{2} (2) \bigg] }}}$

$\:{ \implies{ \sf{k \bigg[ {x}^{2} - \bigg( \frac{ - 1 + 4}{2} \bigg) + \frac{ - 2}{2} \bigg] }}}$

$\: \:{ \implies{ \sf{k \bigg[ {x}^{2} - \bigg( \frac{ 3}{2} \bigg) x - 1\bigg] }}}$

$\: \:{ \implies{ \sf{k \bigg[ \frac{2 {x}^{2} - 3 x- 2}{2} \bigg] }}}$

Now Taking K = 2

$\:{ \implies{ \sf{2 \bigg[ \frac{2 {x}^{2} - 3 x- 2}{2} \bigg] }}}$

$\: \:{ \implies{ \sf{ \cancel{2} \bigg[ \frac{2 {x}^{2} - 3x - 2}{ \cancel{2}} \bigg] }}}$

${ \implies{ \sf{2 {x}^{2} - 3x - 2}}}$

$\: {\large{ \pmb{ \sf{★Final \: Answer... }}}}$

2x² - 3x - 2 is the required polynomial.