Determine Whether the Given Values Are Solutions of the Equation
Question:
Determine whether the given values are solution of the given equation or not:
\[ x^2-3x+2=0 \]
(i) \(x=2\)
(ii) \(x=-1\)
Solution
A value of \(x\) is a solution of an equation if it makes the left-hand side equal to the right-hand side.
Checking \(x=2\)
Substitute \(x=2\) into the equation:
\[ 2^2-3(2)+2 \]
\[ =4-6+2 \]
\[ =0 \]
Since the equation is satisfied, \(x=2\) is a solution.
Checking \(x=-1\)
Substitute \(x=-1\) into the equation:
\[ (-1)^2-3(-1)+2 \]
\[ =1+3+2 \]
\[ =6 \]
Since \(6 \ne 0\), the equation is not satisfied.
Therefore, \(x=-1\) is not a solution.
Answer
\(x=2\) is a solution of the equation, whereas \(x=-1\) is not a solution.
\[ \boxed{x=2 \text{ is a solution and } x=-1 \text{ is not a solution}} \]