Question

if alpha and beta are zeros of x^2+7x+12 find the value of 1÷alpha + 1÷beta -2alpha beta

Answer 1

x² + 7x +12
Alpha + beta = -7
Alpha * beta = 12
I/alpha +1/beta =(al + bet)/all*bet
= -7/12
And 2al.bet = 24
-7/12- 24
= -283/12

Answer 2

Given that $\alpha ,\beta$ are the roots of $x^2+7x+12=0$.

Then $\alpha +\beta =-7,\alpha \beta =12$.

Now the value of the expression $\frac{1}{\alpha} +\frac{1}{\beta} -2\alpha \beta$ is

$\frac{1}{\alpha} +\frac{1}{\beta} -2\alpha \beta =\frac{\alpha +\beta}{\alpha \beta} -2\alpha \beta \\ \frac{1}{\alpha} +\frac{1}{\beta} -2\alpha \beta =\frac{-7}{12} -2(12)=-\frac{295}{12}$