Question

If alfa and beta are the zeros of the polynomial 5x^2+7x+1 . What is the value of alfa^2+beta^2

Answer 1

Answer:

answer need to be 20 character long so just bruh

Answer 2

Answer:

$\green{ { \alpha }^{2} + { \beta }^{2} = \frac{39}{25} }$

Step-by-step explanation:

$\sf \: if \: \alpha \: \: and \: \: \beta \: \: are \: the \: zeroes \: of \: the \: \: \: \: \: \: \: \: \: \: \\ \sf \: polynomial \: \: \: \pink{\bf 5 {x}^{2} + 7x + 1} \: \: \: then \: \: \: \: \: \: \: \: \\ \\ \small{ \bf \: sum \: of \: zeroes \: \: \: \alpha + \beta = - \frac{coefficient \: of \: \: x}{coefficient \: of \: \: {x}^{2} } } \\ \\ \bf \implies \: \red{ \alpha + \beta = - \frac{7}{5} } \\ \\ \bf \: and \\ \\ \small{\bf \: product \: of \: zeroes \: \: \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} } } \\ \red{\bf \implies \: \alpha \beta = \frac{1}{5} } \\ \\ now \\ \\ { \alpha }^{2} + { \beta }^{2} = ( { \alpha + \beta })^{2} - 2 \alpha \beta \\ \\ = {( - \frac{7}{5} })^{2} - 2 \times \frac{1}{5} \\ \\ = \frac{49}{25} - \frac{2}{5} \\ \\ = \frac{49 - 10}{25} \\ \\ = \frac{39}{25}$