1. If `alpha` and `beta` are roots of quadratic equation `3x^2+8x+2=0`, then find the value of `alpha^2+beta^2`

Solution:
`3x^2+8x+2=0`

Comparing the given equation with `ax^2+bx+c=0`

We get `a=3,b=8,c=2`

Sum of roots `=alpha+beta=(-b)/a=(-8)/3`

Product of roots `=alpha*beta=c/a=2/3`

Now we have to find `alpha^2+beta^2`

`alpha^2+beta^2=52/9`

We know that

`alpha^2+beta^2=(alpha+beta)^2-2alphabeta`

`:.alpha^2+beta^2=((-8)/3)^2-2*2/3`

`:.alpha^2+beta^2=64/9-4/3`

`:.alpha^2+beta^2=52/9`

`:.alpha^2+beta^2=52/9`