If (x-3) and (x-1/3) are both factors of f(x) = ax2+5x+b,
then f(3) = 0 and f(1/3) =0
f(3) = a(3)2+5(3)+b = 0 => 9a + b + 15 = 0 ..(i)
f(1/3) = a(1/3)2+5/3+b =0 => a + 9b + 15 =0 ...(ii)
Equation (i) - Equation (ii)
9a + b + 15 - a - 9b - 15 =0
8a - 8b = 0 => a=b
Hence proved