If α and β are two roots of 2 x^2+3 x+1=0 value of α^2+β^2 is:

We have ,

$2 x^2+3 x+1=0$

= $2 x^2+2 x+x+1=0$

= 2x(x + 1) + 1(x + 1)

= (2x + 1) (x + 1)

Now, (2x + 1) = 0

x = -1/2 = alpha

Also, (x + 1) = 0

x = -1 = beta

So, value of $\alpha^2+\beta^2$ = (-1/2 )² + (-1)² = $\frac{5}{4}$