Solve the following quadratic equation by factorization:

$x^2-x-a(a+1)=0$

Given:

Given quadratic equation is $x^2-x-a(a+1)=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$x^2-x-a(a+1)=0$

To factorise $x^2-x-a(a+1)=0$, we have to find two numbers $m$ and $n$ such that $m+n=-1$ and $mn=1(-a(a+1))=-a(a+1)$.

If $m=-(a+1)$ and $n=a$, $m+n=-a-1+a=-1$ and $mn=-(a+1)a=-a(a+1)$.

$x^2-x-a(a+1)=0$

$x^2-(a+1)x+ax-a(a+1)=0$

$x(x-(a+1))+a(x-(a+1))=0$

$(x+a)(x-(a+1))=0$

$x+a=0$ or $x-(a+1)=0$

$x=-a$ or $x=a+1$

The values of $x$ are  $-a$ and $a+1$.

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Updated on: 10-Oct-2022

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