Question

please solve these questions

Answer 1

Hi
17)
According to the remainder theorem

Degree of the remainder < degree of divisor

But in the problem,

Divisor = 2 x + 3

It's degree = 1 ----(1)

Remainder = x - 1

It's degree = 1----(2)

(1) = (2)

It is not possible.

18)
Let p(x) = x^3 + (k+8) x +k

i) if p( x ) divided by ( x- 2 ) the

remainder is p ( 2)

P(2) = 2^3 + (k+8)2 + k

= 8 + 2k + 16 + k

= 24 + 3k -----(1)

ii) if p(x ) divided by (x+1) the remainder should be p(-1)

p(-1) = (-1)^3 + (k+8) (-1) +k

= -1 - k - 8 + k

= -9 ------(2)

According to the problem

Sum of the remainders =0

From (1) and (2)

24 + 3k -9 =0

15 + 3k = 0

3k = - 15

k = ( - 15 )/ 3

k = - 5

Hope this will helps you.