10. x^3 - 5x^2 + 3x + 9 = 0
Rewrite as
x^3 - 5x^2 - 6x + 9x + 9 = 0
x(x^2 - 5x - 6) + 9(x + 1) = 0
x (x - 6)(x + 1) + 9 (x + 1) = 0
(x + 1) [ x (x - 6) + 9 ] = 0
(x + 1) [ x^2 - 6x + 9 ] = 0
(x + 1) (x - 3)(x - 3) = 0
Three real roots.....two equal in value