In each of the following, find the value of $k$ for which the given value is a solution of the given equation:
$x^2-x(a+b)+k=0$, $x=a$

Given:

Given equation is $x^2-x(a+b)+k=0$.

To do:

We have to find the value of $k$ for which $x=a$ is a solution of $x^2-x(a+b)+k=0$.

Solution:

If $x=m$ is a solution of $f(x)$ then $f(m)=0$.  

Therefore,

For $x=a$

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

$(a)^2-a(a+b)+k=0$

$a^2-a^2-ab+k=0$

$k=ab$

The value of $k$ is $ab$.

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Updated on: 10-Oct-2022

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