find the values of A and B so that the polynomial x cube minus 10 X square + a x + b is exactly divisible by x minus 1 as well as X - 2
Answers
Answered by
9
X-1=0
X=1
1) substitute 1 by x
=(1)^3-10(1)^2+a(1)+b = 0 (because they are a factor of the polynomial and remainder = 0)
=1-10+a+b=0
=-9+a+b=0
=a+b=9 ...
Now,
2)x-2=0
X=2
By substituting x by 2
=(2)^3-10(2)^2+a(2)+b=0
=8-10(4)+2a+b=0
=8-40+2a+b=0
=-32+2a+b=0
=2a+b=32 ...
Now subtract 2 by 1
That is : 2a+b-a-b=32-9
a=23
NOW SUBSTITUTE A WITH 23 ON (1)
= 23+b=9
= b=9-24
= b=(-14)
Therefore a=23
b=(-14)
Similar questions