Question

If $\alpha ,\beta$ are the roots of ${2x}^2-x+1=0$, the value of ${\alpha }^2+{\beta }^2$ is :

• A. $1$
• B. $0$
• C. $5/4$
• D. $-3/4$

Answer 1

The correct option is D $-3/4$

Given, $2x^2-x+1=0$

Then $a=2,b=-1$ or $c=1$

$\alpha +\beta =\frac{-b}{a}=\frac{-(-1)}{2}=\frac{1}{2}$

$\alpha \beta =\frac{c}{a}=\frac{\left(1\right)}{2}=\frac{1}{2}$

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

$=(\frac{1}{2}{)}^2-2\left(\frac{1}{2}\right)$

$=\frac{1}{4}-1=-\frac{3}{4}$