Question

if alpha and beta are the zeroes of a polynomial x^2+4x+5 find alpha square+beta square​

Answer 1

Answer:

${ \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ \\ = {( - 4)}^{2} - 2(5) \\ \\ = 16 - 10 \\ \\ = 6.$

Step-by-step explanation:

${x}^{2} + 4x + 5 = 0 \\ \\ \alpha + \beta = - 4 \: \: \: \: \: \: \: \: \alpha \beta = 5 \\ \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ \\ = {( - 4)}^{2} - 2(5) \\ \\ = 16 - 10 \\ \\ = 6.$