If m and n are the roots of the equation $x^2+ax+b=0$ and $m^2$, $n^2$ are the roots of the equation $x^2-cx+d=0$, then which of the following is/are correct? I. $2b-a^2=-c$ II. $b^2=d$ Select the correct answer using the codes given.

For x^2 + ax + b = 0 with roots m and n, the sum is m + n = -a and the product is mn = b. The second equation x^2 - cx + d = 0 has roots m^2 and n^2, so the sum is c = m^2 + n^2 and the product is d = m^2n^2. We can express the sum of squares as c = (m + n)^2 - 2mn, which substitutes to c = a^2 - 2b, meaning 2b - a^2 = -c is correct. Furthermore, since d = m^2n^2 and mn = b, we clearly see that d = b^2, making both statements correct.

• Thanks
• Wrong explanation