Find a quadratic equation of the form ax^2 + bx + c = 0 such that a=2 and (1+ i) is a root.

Since1 + i is a root, it follows that its conjugate1 - i is also a root.

Hence, the sum of the roots, (1 + i) + (1 - i) = 2

              and the product of the roots , (1 + i)(1 - i) =1 - i^2 =2, since i^2 = -1

Recall that given the sum and product of the roots we can find the quadratic equation which is of the form, x^2 - (sum of roots)x + (product of roots) =0

Hence, the quadratic equation is x^2 -2x +2 =0.

But since a quadratic equation of the form ax^2 + bx + c =0, where a =2 is required,simply multiply x^2 -2x +2 =0 by2.

Therefore, the final answer should be 2x^2 -4x +4 =0.