Question

if alpha and betta are zeroes of x square + 5x + 5, find the value of alpha raised to the power -1 and beeeta raised to the power -1

Answer 1

Correct Question :

If alpha and betta are zeroes of x square + 5x + 5, find the value of alpha power -1 + beta power -1

Concepts Required :

Sum of Zeros

• A + B = -b/a

Product of zeros

• A * B = c/a

Note : alpha A and beta B.

Solution :

We have , Equation.

=> x² + 5x + 5.

Let Find the value of,

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

$\tt \mapsto \dfrac{1}{ \alpha } + \dfrac{1}{ \beta }$

$\tt \mapsto \dfrac{ \alpha + \beta }{ \alpha \beta }$

$\tt\mapsto \dfrac{ \frac{ - b}{a} }{ \frac{c}{a} }$

$\tt\mapsto \dfrac{ - b}{c}$

$\tt \mapsto \dfrac{ - 5}{5}$

$\tt \mapsto - 1.$

Therefore, the required value be -1.