2015/102) Two roots of the polynomial $x^3 + ax^2 + 15x -7 = 0$ are equal and rational. Find "a"

If 2 roots are rational then 3rd must be rational.
possible roots are -7 , -1, 1, 7
now product of 2 roots (as same) so roots shall be +1 or - 1 as 7 or -7 cannot be a double root

so 3rd root has to be 7 ( as product has to be +ve)

so $f(x) = x^3 + ax^2 + 15x -7 = 0 = f(7)$

or $343 + 49 a + 105 - 7 = 0$

or $a = 9$

check:
$x^3 - 9x^2 + 15x - 7 = (x-1)^2(x-7)$