Question

$\alpha$
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 :-

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

____________________________

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

Now

$\begin{gathered}\implies \alpha + \beta - \alpha \beta \\ \\ \implies\underline{\red{\boxed{ \sf 4 \sqrt{3} - 3}}}\end{gathered}$