Question-6
(a)if x-2 is a factor of x² + ax +b and a + b = 1, find the values of a and b.
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Answer:
Let p(x)=x
2
+ax+2b
If x+2 is a factor of p(x)
Then by factor theorem
p(−2)=0
⇒(−2)
2
+a(−2)+2b=0
⇒4−2a+2b=0
⇒a−b=2 ---(i)
Also given that a+b=4 ---(ii)
Adiing (i) and (ii) we get
2a=6
⇒a=3
putting a=3 in (i) we get
a−b=2
⇒3−b=2
⇒b=1
Therefore we get a=3 and b=1
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