Question

pls find the roots by using sum and product of roots​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Sum\:of\:zeroes=a^{2}+2}}}$

$\green{\tt{\therefore{Product\:of\:zeroes=a^{3}+1}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt:\implies {x}^{2} - ( {a}^{2} + 2)x + ( {a}^{3} + 1) = 0 \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies Sum \: of \: roots = ?\\ \\ \tt: \implies Product \: of \: roots =?$

• According to given question :

$\tt \circ \: a = 1 \: \: \: \: \: b = - ( {a}^{2} + 2) \: \: \: \: \: c = ( {a}^{3} + 1) \\ \\ \bold{For \: sum \: of \: roots : } \\ \tt: \implies Sum \: of \: roots = \frac{ - b}{a} \\ \\ \tt: \implies Sum \: of \: roots = \frac{ - ( - ( {a}^{2} + 2))}{1} \\ \\ \green{\tt: \implies Sum \: of \: roots = {a}^{2} + 2} \\ \\ \bold{For \: product \: of \: roots : } \\ \tt: \implies Product \: of \: roots = \frac{c}{a} \\ \\ \tt: \implies Product \: of \: roots = \frac{ {a}^{3} + 1}{1} \\ \\ \green{\tt: \implies Product \: of \: roots = {a}^{3} + 1}$

Answer 2

Please see the attachment