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Question
In the following, find the value of k for which the given value is a solution of the given equation:
x2 - x(a + b) + k = 0, x = a
Solution 1
We are given here that,
x2 - x(a + b) + k = 0, x = a
Now, as we know that x = a is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting x = a in the above equation gives us,
x2 - x(a + b) + k = 0
a2 - a(a + b) + k = 0
a2 - a2 - ab + k = 0
k = ab
Hence, the value of k = ab.
Solution 2
We are given here that,
x2 - x(a + b) + k = 0, x = a
Now, as we know that x = a is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting x = a in the above equation gives us,
x2 - x(a + b) + k = 0
a2 - a(a + b) + k = 0
a2 - a2 - ab + k = 0
k = ab
Hence, the value of k = ab.
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