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Question
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Solution
x2 – x(a + b)x + k = 0, x = a
∴ x = a is its solution
∴ (a)2 - a(a + b) + k = 0
⇒ a2 - a2 - ab + k = 0
⇒ -ab + k = 0
∴ k = ab.
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