Question

if alpha and beta are zeros of P of x is equal to 2 x square - x minus 6 then find the value of Alpha power minus 1 plus beta the power minus 1

Answer 1

I hope it would help you

Answer 2

To find
$\frac{1}{ \alpha } + \frac{1}{ \beta }$
${ \alpha }^{ - 1} + { \beta }^{ - 1} can \: be \: written \: as \\ \frac{1}{ \alpha } + \frac{1}{ \beta }$


P ( x ) = 2x² - x - 6


• Sum of Zeros
$= \frac{ - coefficient \: ofx}{coefficient \: of \: {x}^{2} }$


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

• Product of Zeros
$= \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

$\alpha \beta = \frac{ - 6}{2} \\ \alpha \beta = \frac{ - 3}{1}$


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

$= \frac{ \frac{1}{2} }{ - 3}$

=
$\frac{1}{2} \times \frac{1}{ - 3}$

$= \frac{ - 1}{6}$