Determine Whether the Given Values Are Solutions of the Equation
Question:
Determine whether the given values are solution of the given equation or not:
\[ x^2+x+1=0 \]
(i) \(x=0\)
(ii) \(x=1\)
Solution
A value of \(x\) is a solution of an equation if it makes the left-hand side equal to zero.
Checking \(x=0\)
Substitute \(x=0\) into the equation:
\[ 0^2+0+1 \]
\[ =1 \]
Since \(1 \ne 0\), \(x=0\) is not a solution.
Checking \(x=1\)
Substitute \(x=1\) into the equation:
\[ 1^2+1+1 \]
\[ =3 \]
Since \(3 \ne 0\), \(x=1\) is not a solution.
Answer
Neither \(x=0\) nor \(x=1\) satisfies the equation.
\[ \boxed{x=0 \text{ is not a solution and } x=1 \text{ is not a solution}} \]