If one root of `x^2-6kx +5=0` is 5, find the value of k

Options

A. `-(1)/(2)`
B. `-1`
C. 1
D. 2

Answer

To solve the problem, we need to find the value of \( k \) given that one root of the quadratic equation \( x^2 - 6kx + 5 = 0 \) is \( 5 \).

### Step-by-Step Solution:

1. **Substitute the root into the equation**: Since one root is \( 5 \), we can substitute \( x = 5 \) into the equation.
\[ 5^2 - 6k(5) + 5 = 0 \]

2. **Calculate \( 5^2 \)**: We know that \( 5^2 = 25 \).
\[ 25 - 6k(5) + 5 = 0 \]

3. **Combine like terms**: Now, simplify the equation by combining \( 25 \) and \( 5 \).
\[ 30 - 30k = 0 \]

4. **Isolate \( k \)**: Move \( 30k \) to the other side of the equation.
\[ 30 = 30k \]

5. **Solve for \( k \)**: Divide both sides by \( 30 \).
\[ k = \frac{30}{30} = 1 \]

### Final Answer:
The value of \( k \) is \( 1 \).

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