Question

Write the zeroes of the polynomial $x^2+2x+1$.

Answer 1

Find the zeroes of the polynomial

Let $p\left(x\right)=x^2+2x+1$,

$\begin{array}{rcl}p\left(x\right)& =& x^2+2x+1\\ & =& x^2+x+x+1\\ & =& x(x+1)+1(x+1)\\ & =& (x+1)(x+1)\end{array}$

The value of the polynomial $p\left(x\right)=0$

$$\begin{gathered} \Rightarrow (x+1)(x+1)=0 \\ \Rightarrow (x+1)=0,(x+1)=0 \\ \Rightarrow x=-1,x=-1 \end{gathered}$$

Hence, the polynomial $p\left(x\right)=$ $x^2+2x+1$has repeated zeroes$-1$.