Question

plz help,, do it fast ​

Answer 1

Hey mate ,

Kindly find the attachment!!!

It is not clear that polynomial have 7 as it's constant or 1 .

I have taken 7 .

If it would be 1 . Then kindly put the value of c as 1 instead of 7 .

Hope you find it helpful!!!!!

Do mark it as brainliest!!!!

Answer 2

$\alpha \: and \: \beta$ are roots of the equation:

3x² + 5x +7 = 0

hence,

$\alpha + \beta = - \frac{b}{a} = \frac{ - 5}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i)\\ \\ \alpha \beta = \frac{c}{a} = \frac{7}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (ii)$

now,

$\: \: \: \: \frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} } \\ = \frac{ { \alpha }^{2} + { \beta }^{2} }{ { \alpha }^{2} { \beta }^{2} } \\ = \frac{ {( \alpha + \beta )}^{2} - 2 \alpha \beta }{ {( \alpha \beta )}^{2} } \\ = \frac{ {( \frac{ - 5}{3} )}^{2} - 2( \frac{7}{3} )}{ {( \frac{7}{3} )}^{2} } \\ = \frac{ \frac{25}{9} - \frac{14}{3} }{ \frac{49}{9} } = \frac{ \frac{25}{9} - \frac{42}{9} }{ \frac{49}{9} } \: \: \: \: \: \: ... \: (from \: i \: and \: ii) \\ = \frac{ \frac{25 - 42}{9} }{ \frac{49}{9} } = \frac{ \frac{ - 17}{9} }{ \frac{49}{9} } \\ = \frac{ - 17}{49}$

Hence,

$\frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} } = \frac{ - 17}{49}$