Answer :

Let f (x) = x3+ax2-bx+10 and g (x) = x2-3x+2 be the given polynomials.

We have g (x) = x2-3x+2 = (x – 2) (x – 1)


Clearly, (x -1) and (x – 2) are factors of g (x)


Given that f (x) is divisible by g (x)


g (x) is a factor of f (x)


(x – 2) and (x – 1) are factors of f (x)


From factor theorem,


If (x – 1) and (x – 2) are factors of f (x) then f (1) = 0 and f (2) = 0 respectively.


f (1) = 0


(1)3 + a (1)2 – b (1) + 10 = 0


1 + a – b + 10 = 0


a – b + 11 = 0 (i)


f (2) = 0


(2)3 + a (2)2 - b (2) + 10 = 0


8 + 4a – 2b + 10 = 0


4a – 2b + 18 = 0


2 (2a – b + 9) = 0


2a – b + 9 = 0 (ii)


Subtract (i) from (ii), we get


2a – b + 9 – (a – b + 11) = 0


2a – b + 9 – a + b – 11 = 0


a – 2 = 0


a = 2


Putting value of a in (i), we get


2 – b + 11 = 0


b = 13


Hence, a = 2 and b = 13


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