When polynomial bx2 + x + 5 is divided by (x – 3), the remainder is m.
∴ By remainder theorem,
Remainder = p(3) = m
p(x) = bx2 + x + 5
∴ p(3) = b(3)2 + 3 + 5
∴ m = b(9) + 8
m = 9b + 8 …(i)
When polynomial bx3 – 2x + 5 is divided by x – 3 the remainder is n
∴ remainder = p(3) = n
p(x) = bx3 – 2x + 5
∴ P(3) = b(3)3 – 2(3) + 5
∴ n = b(27) – 6 + 5
∴ n = 27b – 1 …(ii)
Now, m – n = 0 …[Given]
∴ m = n
∴ 9b + 8 = 27b – 1 …[From (i) and (ii)]
∴ 8 + 1 = 27b – 9b
∴ 9 = 18b
∴ b = 1/2