Answer :

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


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