Mathematics
If x - 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Factorisation
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Answer
Given,
x - 2 is a factor of x2 + ax + b.
Hence, on substituting x = 2 in x2 + ax + b, remainder = 0.
⇒ (2)2 + a(2) + b = 0
⇒ 4 + 2a + b = 0
⇒ b = -(2a + 4)
Substituting value of b in a + b = 1 we get,
⇒ a + -(2a + 4) = 1
⇒ a - 2a - 4 = 1
⇒ -a - 4 = 1
⇒ -a = 1 + 4
⇒ a = -5.
⇒ b = -(2a + 4) = -[2(-5) + 4] = -(-10 + 4) = 6.
Hence, a = -5 and b = 6.
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