Question

Solve the following quadratic equation by factorization :
$x^2$ - x - a(a + 1) = 0

The roots are$-a,a+1$

• A. True
• B. False

Answer 1

The correct option is A True

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

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

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

$\Rightarrow$ $x[x-(a+1\left)\right]+a[x-(a+1\left)\right]=0$

$\Rightarrow$ $[x-(a+1\left)\right][x+a]=0$

$\Rightarrow$ $x-(a+1)=0$ and $x+a=0$

$\therefore$ $x=(a+1)$ and $x=-a$

$\therefore$ We can see, roots given in question are correct.