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:
\[ x^2+3ax+k=0 \]
Given, \[ x=-a \]
Solution
Since \(x=-a\) is a solution, it must satisfy the given equation.
Substituting \(x=-a\) into the equation:
\[ (-a)^2+3a(-a)+k=0 \]
\[ a^2-3a^2+k=0 \]
\[ -2a^2+k=0 \]
\[ k=2a^2 \]
Answer
Therefore, the required value of \(k\) is
\[ \boxed{k=2a^2} \]
Hence, when \(k=2a^2\), the value \(x=-a\) satisfies the equation \(x^2+3ax+k=0\).