Find the Value of k for which the Given Value is a Solution
Question:
Find the value of \(k\) for which the given value is a solution of the equation:
\[ kx^2+\sqrt2\,x-4=0 \]
Given, \[ x=\sqrt2 \]
Solution
Since \(x=\sqrt2\) is a solution, it must satisfy the equation.
Substituting \(x=\sqrt2\) into the equation:
\[ k(\sqrt2)^2+\sqrt2(\sqrt2)-4=0 \]
\[ 2k+2-4=0 \]
\[ 2k-2=0 \]
\[ 2k=2 \]
\[ k=1 \]
Answer
Therefore, the required value of \(k\) is
\[ \boxed{k=1} \]
Hence, when \(k=1\), the value \(x=\sqrt2\) satisfies the equation \(kx^2+\sqrt2\,x-4=0\).