Question

If α and β are the zeroes of the polynomial x²+3x+7,then α²+β² is equal

Answer 1

Answer:

$\alpha + \beta = - 3 \: \: \ \alpha \beta = 7 \\ { \alpha }^{2} + { \beta }^{2} = { (\alpha + \beta )}^{2} - 2 \alpha \beta = 9 - 14 \\ = - 5$

hope it helps

Mark me as brainliest

Answer 2

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

$\green{\tt{\therefore{\alpha^{2}+\beta^{2}=-5}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} + 3x + 7 = 0 \\ \\ \tt: \implies \alpha \: and \: \beta \: are \: zeroes \\ \\ \red{\underline \bold{To \: Dind :}} \\ \tt: \implies { \alpha }^{2} + { \beta }^{2} = ?$

• According to given question :

$\tt \circ \: a = 1 \: \: \: \: \: \: b = 3 \: \: \: \: \: \: c = 7 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Sum \: of \: zeroes = \frac{ -b}{a} \\ \\ \tt: \implies \alpha + \beta = \frac{ - 3}{1} - - - - - (1) \\ \\ \bold{Similarly : } \\ \tt: \implies Product \: of \: zeroes = \frac{c}{a} \\ \\ \tt: \implies \alpha \beta = \frac{7}{1} - - - - - (2)\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies { \alpha }^{2} + { \beta }^{2} = { (\alpha + \beta )}^{2} - 2 \alpha \beta \\ \\ \tt: \implies { \alpha }^{2} + { \beta }^{2} = {3}^{2} - 2 \times 7 \\ \\ \tt: \implies { \alpha }^{2} + { \beta }^{2} = 9 - 14 \\ \\ \green{\tt: \implies { \alpha }^{2} + { \beta }^{2} = - 5}$