Question

If
$\alpha$
and
$\beta$
are the zeroes of a Polynomial x²-4
$\sqrt{3} x$
+ 3 then find value of
$\alpha + \beta - \alpha \beta$
​

Answer 1

Given :-

$\longrightarrow \sf {x}^{2} - 4 \sqrt{3} x + 3$

To Find :-

$\longrightarrow \sf Value \: of \: \alpha + \beta - \alpha \beta$

Solution :-

$\implies \sf \alpha + \beta = \frac{ - b}{a} \\ \\ \implies \sf \alpha + \beta = \frac{ - ( - 4 \sqrt{3}) }{1} \\ \\ \implies \sf \alpha + \beta = 4 \sqrt{3}$

_______________________

$\implies \sf \alpha \beta = \frac{c}{a} \\ \\ \implies \sf \alpha \beta = \frac{3}{1} \\ \\ \implies \sf \alpha \beta = 3$

Now

$\implies \alpha + \beta - \alpha \beta \\ \\ \implies\underline{\boxed{ \sf 4 \sqrt{3} - 3}}$