CBSE Class 9 Answered
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 + ax 22 + b x 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 + ax 32 + b x 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.