Question

if alpha and beta are the zeores of the polynomial x square +7x+12 find the value of 1/alpha +1/beta -2alphabeta

Answer 1

$x {}^{2} + 7x + 12$

$x {}^{2} + 4x + 3x + 12$

$x(x + 4) + 3(x + 4)$

$(x + 3)(x + 4)$

Hence x = -3 and -4

$so \: \: \alpha = - 3 \: \: \: \beta = - 4$

$(1 \div \alpha ) + (1 \div \beta ) - 2 \alpha \beta$

Now put value

- 1/3 + (- 1/ 4) - 2 (-3)(-4)

-1/3 - 1/4 - 24

( -4 - 3 - 288 ) / 12

= -295 / 12


Thanks

Answer 2

$x {}^{2} + 7x + 12$

$x {}^{2} + 4x + 3x + 12$

$x(x + 4) + 3(x + 4)$

$(x + 3)(x + 4)$

Hence x = -3 and -4

$so \: \: \alpha = - 3 \: \: \: \beta = - 4$

$(1 \div \alpha ) + (1 \div \beta ) - 2 \alpha \beta$

Now put value

- 1/3 + (- 1/ 4) - 2 (-3)(-4)

-1/3 - 1/4 - 24

( -4 - 3 - 288 ) / 12

= -295 / 12


Thanks