Sum and Product of Roots ... ?

If the roots of a quadratic are A and B then working backwards from x=A and x=B means (x-A)(x-B) = 0 then expanding: x^2 -(A+B)x +AB =0. So in any quadratic with one x^2 the coefficient of x is minus the sum of the roots and the constant is the product of the roots. You can use this fact to form the equation. (1) sum = 4/3, product = - 1/6 equation is x^2 -4x/3 -1/6 = 0. Tidy this up by multiplying through by 6: 6x^2 - 8x -1 = 9. (2) I presume here you are being given the two roots, A=4+rt3 and B= 4-rt3. that would give sum A+B = 8 and product AB = (4+rt3)(4-rt3) =16 - 3 =13 so the equation is x^2 -8x + 13 = 0. It was not clear, but if (1) was giving you the two roots, use this method shown for (2) to obtain the equation.