Answer :

We have,

p (x) = 2x3 + ax2 + 3x – 5


q (x) = x3 + x2 – 4x + a


It is given in the question that, when p (x) and q (x) is divided by (x – 2) it leaves same remainder


p (2) = q (2)


2 (2)3 + a (2)2 + 3 (2) – 5 = (2)3 + (2)2 – 4 (2) + a


2 × 8 + a × 4 + 3 × 2 – 5 = 8 + 4 – 4 × 2 + a


16 + 4a + 6 – 5 = 12 – 8 + a


16 + 4a + 1 = 4 + a


4a – a = 4 – 17


3a = - 13


a =


Hence proved


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