r and s are the roots of 3x^2 + 4x - 12 = 0. Find r^2+s^2+2rs
Divide 3x2+4x−12=0 by 3: x2+43x−4=0 ...(1)
Quadratic with roots r and s: (x−r)(x−s)=0 or x2−(r+s)x+rs=0 ...(2)
Compare (1) and (2) to see that r+s=−43 ...(3)
Note that r2+s2+2rs=(r+s)2
Now it should be easy to answer the question.