Question

8. If ax+ bx + c and br? + ax + c have a common factor x + 1 then show that
c=0 and a = b.

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Answer 1

G(x) = x +1
0= x+ 1
x = -1
Substituting G (-1) in P(x) and Q (x), we get
a(-1)^2 + b(-1) + c = b(-1)^2 + a(-1) + c
Therefore,
a - b + c = b - a + c
As a - b = b- a, b = a
Also, c = 0 as a - b + c = b - a + c = 0
As a - b and a+ b = 0 thus c = 0