Question

Please try to do this sum​

Answer 1

(1) Given Polynomial :

$a {x}^{2} + bx + c$

And Zeroes :

$\alpha \: and \: \beta$

As we know that :

Sum of Zeroes = -b/a

and product of zeroes = c/a

To find :

$\frac{1}{ \alpha } + \frac{1}{ \beta }$

$= > \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ = > \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ = > \frac{ \frac{ - b}{a} }{ \frac{c}{a} } \\ \\ = > \frac{ - b}{c}$

(2) Given polynomial :

${x}^{2} + 7x + 7$

Where a = 1, b = 7 and c = 7

And zeroes :

$\alpha \: and \: \beta$

As we know that :

Sum of Zeroes = -b/a = -7/1 = -7

and product of zeroes = c/a = 7/1 = 7

To find :

$\frac{1}{ \alpha } + \frac{1}{ \beta} - 2 \alpha \beta$

$= > \frac{ \beta + \alpha }{ \alpha \beta } - 2\alpha \beta \\ \\ = > \frac{ \alpha + \beta }{ \alpha \beta } - 2 \alpha \beta \\ \\ = > \frac{ - 7}{7} - 2 \times 7 \\ \\ = > - 1 - 14 = - 15$

Hope it helps ☺

Fóllòw Më ❤