Question

If alpha and beta are the zeroes of the polynomial 3x^2+2x+3 then, find 1/(alpha)^2+1/(beta)^2

Answer 1

Answer:

643+4567-77+1173

672+177272

Answer 2

$\large \green{ \underline{answer \: \: = \: \frac{ - 14}{9} }} \\ \\ \large \implies{ \underline{solution}} \\ \\ \large \implies{3 {x}^{2} + 2x + 3 = 0 } \\ \\ \large \implies{sum \: \: of \: \: roots \: = \frac{ - b}{a} = \frac{ - 2}{3} } \\ \\ \large \implies{product \: \: of \: roots \: = \frac{c}{a} = 1} \\ \\ \large \implies \orange{ \underline{to \: \: find \: }} \\ \\ \large \implies{ \frac{1}{ { \alpha }^{2} } + \frac{1}{ \beta {}^{2} } } \\ \\ \large \implies{ \frac{ { \beta }^{2} + { \alpha }^{2} }{ { \alpha }^{2} { \beta }^{2} } } \\ \\ \large \implies{ \frac{( \alpha + \beta ) {}^{2} - 2 \alpha \beta }{( \alpha \beta ) {}^{2} } } \\ \\ \large \implies{ \frac{ (\frac{ - 2}{3} ) {}^{2} - 2(1)}{1} } \\ \\ \large \implies{ \frac{ \frac{4}{9} - 2}{1} } \\ \\ \large \implies{ \boxed{\frac{ - 14}{9} }}$