Question

What is the quadratic equation when roots are a+b and a-b?

Answer 1

The easiest way (I believe)
If p and q are the roots, the equation should be of the form
${x}^{2} - (p + q)x + pq$
Therefore in your case
${x}^{2} - (a + b + a - b)x + ((a + b)(a - b)) = \\ {x}^{2} - 2ax + {a}^{2} - {b}^{2}$
Hope this helps.