If(x3+ax2+bc+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3), find the value of a and b.
If(x3+ax2+bc+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3), find the value of a and b.
Dear student, 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.
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.
