Question

Determine whether the given values are a solution of the given equations or not.

$x^2-x+1=0;x=1,x=-1$

Answer 1

Step 1:

Given equation: $x^2-x+1=0$.

Let the equation be denoted by $p\left(x\right)=0$

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

Put $x=1$ in the given equation.

$$\begin{gathered} p\left(1\right)={\left(1\right)}^2-1+1 \\ p\left(1\right)=1-1+1 \\ p\left(1\right)=1 \end{gathered}$$

Thus, $p\left(1\right)\ne 0$.

Hence, $x=1$ is not a solution to the given equation.

Step 2:

Put $x=-1$ in the given equation.

$$\begin{gathered} p\left(-1\right)={\left(-1\right)}^2-\left(-1\right)+1 \\ p\left(-1\right)=1+1+1 \\ p\left(-1\right)=3 \end{gathered}$$

Thus, $p\left(-1\right)\ne 0$.

Hence, $x=-1$ is not a solution to the given equation.

Therefore, $x=1$ and $x=-1$ are not the solutions to the given quadratic equation.