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The roots of the equation $x^{2} -3x-m( m+3) =0$, where m is a constant, are:
$( A) m, m+3$
$( B)-m, m+3$
$( C)m, -(m+3)$
$( D)-m,-(m+3)$
Given: equation $x^{2} -3x-m( m+3) =0$
To do: To find out the roots of the given equation.
Solution:
$x^{2} -3x-m( m+3) =0$
$\Rightarrow x^{2} -( m+3) x+mx-m( m+3) =0$
$\Rightarrow x( x-( m+3)) +m( x-( m+3) =0$
$\Rightarrow ( x+m)( x-( m+3)) =0$
If $( x+m) =0$
$\Rightarrow x=-m$
If $x-( m+3) =0$
$\Rightarrow x=m+3$
$\therefore \ x=-m,m+3$
$\therefore$ Option $( A)$ is correct.
Updated on: 10-Oct-2022
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