Concept:The Standard Form of a Quadratic Equation is ax2 + bx + c = 0Sum of roots = ?b/aProduct of roots = c/aFormulae (? - ?)2 + 4.?.? = (? + ?)2 Calculation:Given:x2 - 8x + q = 0 and ?2 - ?2 = 16Sum of roots = ? + ? = ?b/a = -(- 8) = 8 ------(i)Product of roots = ?.? = q ------(ii)We have ?2 - ?2 = 16? (? + ?)(? - ?) = 16? 8 × (? - ?) = 16? (? - ?) = 2 ------(iii)We know that, (? - ?)2 + 4.?.? = (? + ?)2 Putting the value of equation (i), (ii) and (iii), we get,? 22 + 4q = 82? 4q = 64 - 4 = 60? q = 15? The value of q is 15