#### Question

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} - x(a + b) + k = 0, x = a

#### Solution 1

We are given here that,

x^{2} - 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,

x^{2} - x(a + b) + k = 0

a^{2} - a(a + b) + k = 0

a^{2} - a^{2} - ab + k = 0

k = ab

Hence, the value of k = ab.

#### Solution 2

We are given here that,

x^{2} - 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,

x^{2} - x(a + b) + k = 0

a^{2} - a(a + b) + k = 0

a^{2} - a^{2} - ab + k = 0

k = ab

Hence, the value of k = ab.