Find the roots of the equation $x^{2}-3x-m( m+3)=0$.

Given: Equation $x^{2}-3x-m( m+3)=0$.

To do: To find the roots of the given equation.

Solution:

Given equation is: $x^{2}-3x-m( m+3)=0$.

$\Rightarrow x^{2}-3x-m^{2}-3m=0$

$\Rightarrow x^{2}-m^{2}-3x-3m=0$

$\Rightarrow ( x-m)( x+m)-3( x+m)=0$

$\Rightarrow ( x+m)( x-m-3)=0$

If $x+m=0$

$\Rightarrow x=-m$

If $x-m-3=0$

$\Rightarrow x=m+3$

$\therefore x=m,\ m+3$.

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Updated on: 10-Oct-2022

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