Question

Given that p(x) where p(x) = x³ + 3x² + kx + 4 , where 'k' is constant such that reminder on dividing p(x) by (x - ) is 3 times the reminder on dividing by (x + 1) , find the value 'k'

a) - 9/2
b) 5/2
c) - 2/3
d) none of these

Answer 1

P( x ) = x³ + 3x² + kx +4

case 1 :- when we divide P(x ) by (x -1) then reminder will be
x = 1 put in P(x )
P( 1 ) = (1)³ +3(1)² + K (1) + 4
= K + 8

hence reminder will be ( K + 8)

case 2 :- similarly if P(x ) divide by (x +1)
then, reminder will be ,
x = -1 put in P(x )

P (-1) = (-1)³ +3(-1)² + K(-1) + 4

= -1 +3 -K + 4

= 6 - K

hence, reminder now ( 6 - K)

question says that ,

( K + 8) = 3( 6 - K )

K + 8 = 18 - 3k

4k = 10

K = 5/2

so, option (b) is correct