Question

If $\alpha$ and $\beta$ are the roots of the equation $3x^2-2x-8=0$, find the value of ${\alpha }^2-\alpha \beta +{\beta }^2$.

• A. $\frac{76}{9}$
• B. $\frac{25}{3}$
• C. $\frac{16}{3}$
• D. $\frac{32}{3}$

Answer 1

The correct option is A $\frac{76}{9}$

$3x^2-2x-8=0$

sum of roots$=\alpha +\beta =-\frac{-2}{3}=\frac{2}{3}$

product of roots$=\alpha \beta =\frac{-8}{3}$

${\alpha }^2-\alpha \beta +{\beta }^2=(\alpha +\beta {)}^2-3\alpha \beta$

$=(\frac{2}{3}{)}^2-3(\frac{-8}{3})$

$=\frac{4}{9}+8$

$=\frac{76}{9}$

So, the answer is option (A)