If x2 + 3x + 5 = 0 and ax2 + bx + c = 0 have a
common root and a, b, c ∈ N, then the minimum
value of a + b + c is…….

Dear student,

The minimum value of a+b+c is zero....

As roots of x2 + 3x + 5 are non-real so both roots
are common
a + b + c = 9λ

x2+3x+5=ax2+bx+c

x2(1-a)+x(3-b)+5-c=0

by  putting  x=1,,   1-a+3-b+5-c=0

so  a+b+c=9