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Question
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Solution
x2 + 4x – 5 = 0 , x = 1, –1
For x = 1
\[ \left( 1 \right)^2 + 4\left( 1 \right) - 5 = 0\]
\[ \Rightarrow 1 + 4 - 5 = 0\]
\[ \Rightarrow 5 - 5 = 0\]
So, x = 1 is a solution of the given equation.
For x = –1
\[\left( - 1 \right)^2 + 4\left( - 1 \right) - 5 = 0\]
\[ \Rightarrow 1 - 4 - 5 = 0\]
\[ \Rightarrow - 3 - 5 = 0\]
\[ \Rightarrow - 8 \neq 0\]
So, x = –1 is not a solution of the given equation.
Thus, only x = 1 is root of the given equation.
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