Question
Sun December 16, 2012 By:

Find a and b such that x+1 and x+2 are factors of the polynomial x3 + ax2 -bx+10

Expert Reply
Sun December 16, 2012
Let p(x) = x3 + ax2 -bx+10
 
x+1 is a factor of p(x), so p(-1) = 0
-1 + a + b + 10 = 0 or a + b + 9 = 0                 ... (1)
 
x+2 is a factor of p(x), so p(-2) = 0
-8 + 4a + 2b + 10 = 0 or 2a + b + 1 = 0            ... (2)
 
Solve equations (1) and (2) to get the required values of a and b.
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