Question

8. The polynomials ax^3 + 3x^2 – 3 and 2x^3- 5x
+ a, when divided by x - 4, leave the same
remainder in each case. Find the value of a.​

Answer 1

when equation is divided by (x-4) remainder will be f(x)

first we will put x = 4 in equation first , and find its remainder

f(4) = a*4³ + 3*(4)² - 3

= 64a +48 - 3

= 64a + 45 [Remainder 1]

Now, we put again x = 4 in second equation ,

f(4) = 2*4³ - 5*4 + a

= 128 -20 + a

= 108 + a [ Remainder 2]

since , remainder is same in each case ,

64a + 45 = 108 + a

63a = 63

a = 1 [Ans.]

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