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Question
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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Solution
Let f(x) = x2 + ax + b
Since, (x – 2) is a factor of f(x).
∴ Remainder = f(2) = 0
(2)2 + a(2) + b = 0
4 + 2a + b = 0
2a + b = – 4 ...(i)
It is given that:
a + b = 1 ...(ii)
Subtracting (ii) from (i), we get,
a = –5
Substituting the value of a in (ii), we get,
b = 1 – (–5) = 6
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