Question

Match the following to their roots.

• A. $x=0,x=-1$
• B. $x=-1$
• C. $x=0,x=-3$
• D. $x=-1,x=-2$

Answer 1

Let's solve the given equations.

1. $x^2+3x+2=0$

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

2. $x^2+2x+1=0$

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

3. $x^2+x+0=0$

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

4. $x^2+3x+0=0$

$\Rightarrow$ $x^2+3x+0x+0=0$
$\Rightarrow$ $x(x+3)+0(x+1)=0$
$\Rightarrow$ $x(x+3)=0$
$\Rightarrow$ $x=0,x=-3$