Q13/026) 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 the double root shall be +1 or - 1 as 7 or -7 shall give product module 49 or more.

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)

alternatively we have(x-1)^2(x-7) and multiplying we get  x^3 - 9x^2 + 15x - 7 or a = 9