Question

if alpha, beta are zeros of x square + 5 x + 5 find the value of alpha power -1 + beta power -1

Answer 1

Given↘️

p(x) = x² + 5x +5

Here,

a = 1

b = 5

c = 5

And zeros of p(x) are

$\alpha and \: \beta$

To find :-

${ \alpha }^{ - 1} + { \beta }^{ - 1}$

We know that ,

$\alpha + \beta = \frac{ - b}{a} \\ = > \alpha + \beta = - 5 ........(i)$

Also,

$\alpha \beta = \frac{c}{a} \\ = > \alpha \beta = 5 \: .......(ii)$

Solution ➡️

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

Putting the values obtained in equation (i) and (ii)

We get,

$\frac{ \beta + \alpha }{ \alpha \beta } = \frac{ - 5}{5} = - 1$

Hence,

${ \alpha }^{ - 1} + { \beta }^{ - 1} = - 1$