What is the product of sum of roots and product of roots of below quadratic equation : x2 - 5x + 6 = 0

Question

Solve for the parameter a for which the sum of all of the real valued roots to the equation sin(√(ax – x2)) = 0 is exactly equal to 100.

Answer 1

x^2 + 5x + 6 = 0
x^2 + 3x + 2x + 6 = 0
x(x + 3) + 2(x + 3) = 0
(x + 3)(x + 2) = 0
x = -3, -2.
(-3 + (-2))*((-3)(-2))
(SUM OF ROOTS)*(PRODUCT OF ROOTS) = (-5)(6) = -30.