Question

If α and β are the roots of the quadratic equation 3x^2-4x+7=0 find 1/α^2 + 1/β^2

Answer 1

3x^2-4x+7 has roots
a=(2+i√17)/3 and b=(2-i√17)/3
so 1/a^2 + 1/b^2 = -26/49