Question

If alpha and beta are the zeroes of polynomial x 2-7x+7,find the value of 1/alpha +1/beta - 2 alpha beta

Answer 1

The given quadratic equation is:
$x^{2} -7x+7=0$
Using the formula:
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
we get, 
$\alpha =\frac{7+\sqrt{21}}{2} \\ \beta =\frac{7-\sqrt{21}}{2}$
$\frac{1}{ \alpha } + \frac{1}{ \beta } -2 \alpha \beta =-13$