• 0
Guru

# (x – 2) is a factor of the expression x 3 +ax 2 +bx+6. when this expression is divided by (x – 3) , it leaves the remainder 3. find the values of a and b.

• 0

An important question from examination point of as it has been already asked in previous year paper of 2005 in which we are asked to find the values of a and b if (x – 2) is a factor of the expression x3+ax2+bx+6. when this expression is divided by (x – 3) , it leaves the remainder 3

Share

1. Let p(x) = x3 + ax2 + bx +6

(x-2) is a factor of the polynomial x3 + ax2 + b x +6

p(2) = 0

p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0

7 +2 a +b = 0

b = – 7 -2a -(i)

x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.

p(3)=3

p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3

11+3a +b =1

=> 3a+b =-10

=> b= -10-3a -(ii)

Equating the value of b from (ii) and (i) , we have

(- 7 -2a) = (-10 – 3a)

a = -3

Substituting a = -3 in (i), we get

b = – 7 -2(-3)

= -7 + 6

= -1

Thus the values of a and b are -3 and -1 respectively.

• 0