If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.

If a is a root of the equation x² – (a + b)x + k = 0, find the value of k.

Sum

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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