Question

Using the remainder theorem find the reminders obtained when x³+(Kx+8)x+k is divided by x+1 and x-2.
Hence find k if the sum of the remainders is 1.​

Answer 1

To find:-

k if the sum of the remainders is 1.

Solution:-

Let,

f(x) = x + (kx+8)x+k

when f(x) is divided by (x + 1) by Remainder theorem

Remainder,

=> f(-1) = (-1)³+{k (-1)+8)} (-1) + k

=> f(-1) = -1+(-k + 8) (-1)+k

=> f(-1)= -1+k-8+k

=> f(-1) = 2k-9

when f (x) is divided by (x - 2),

Remainder,

=> f(2) = (2) + (k.2 + 8) 2+ k

=> f(2) =b8+4k+16+k

=> f(2) = 5k + 24

Also, sum of remainders = 1

=> f(-1) + f(2) = 1

=> 2k - 9 +5k + 24 = 1

=> 7k + 15 = 1

=> 7k =1-15

=> k = -14/7

=> k =-2

✶⊶⊷⊶⊷❍•♦•❍⊶⊷⊶⊷✶

♦ llBrainPowerll ♦