Let f(x) = x³ – 10x² + ax + b

Now,

By using factor theorem,

(x – 1) and (x - 2) will be the factors of f(x) if f(1) = 0 and f(2) = 0

Hence,

f(1) = 1³ – 10 (1)² + a × 1 + b
0 = 1 – 10 + a + b

a + b = 9 (i)

And,

f(2) = 2³ – 10 × 2² + a × 1 + b

0 = 8 – 40 + 2a + b

2a + b = 32 (ii)

Now, subtracting (i) from (ii)

a = 23

Using the value of a in (i), we get

23 + b = 9

b = 9 – 23

b = -14

Hence,

a = 23 and b = -14