Hey,

         use the remainder theorem/ the vanishing factor method.

Divisor in the first case is 2x-1.

so put x= -1/2

you will get the remainder as (4b-a+18)/8 which is equal to 5

solving this, you get

4b-a=22.....................................[1]

In the second case f'(x) = 3ax²+10x - b

divisor= 3x-1

Using the same method as above:-

Remainder is (10+a-3b)/3 and this is = 0 as it is perfectly divisible.

solving this, you get

a - 3b = -10................................[2]

solving equations [1] and [2] ,

you get a=26 and b=12

 

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