The quadratic equation 2x^2+8x+1=0 has roots a and b. Write down the value of a+b and ab and a^2+b^2.

Since the quadratic has roots a and b, this means it can be fatored as 2(x-a)(x-b)=0. Expanding this out we get 2x^2-2(a+b)x+2ab=0 and matching the coefficients for the terms x^1 and x^0 we get a+b=-4 and ab=1/2. Now, if we take (a+b)^2 this expands to a^2+b^2+2ab so a^2+b^2=(a+b)^2-2ab=4^2-2*1/2=15