Question

if alpha and beta are the zeroes of quadratic polynomial f(x)=xsquare-5x+4 find the value of 1/alpha+1/beta-2alpha beta

Answer 1

We know,
$If \alpha \: \beta \: are \: the \: two \: roots \: of \: a \\ quadratic \: equation, \: then$
${x}^{2} - (\alpha + \beta )x + \alpha \beta = 0$
$Here, \\ {x}^{2}-5x+4=0$
$So here, \\ (\alpha+\beta)=5, and \\ (\alpha \beta)=4 \\ We \: have \: to \: find \: the \: value \: of \\ (\frac{1}{\alpha}+\frac{1}{\beta}-2 \alpha \beta)$
$\frac{\alpha + \beta}{\alpha \beta}-2 \alpha \beta$
Putting in the values, we get
$\frac{5}{4}-2(4) \\ = \frac{-27}{4}$