If one of the roots of quadratic equation `7x^2-50x+k = 0` is `7`, then what is the value of `k` ?

Options

A. `7`
B. `1`
C. `50/7`
D. `7/50`

Answer

To find the value of \( k \) in the quadratic equation \( 7x^2 - 50x + k = 0 \) given that one of the roots is \( 7 \), we can follow these steps:

### Step-by-Step Solution:

1. **Substitute the Root into the Equation**: Since \( 7 \) is a root of the equation, we can substitute \( x = 7 \) into the equation:
\[ 7(7^2) - 50(7) + k = 0 \]

2. **Calculate \( 7^2 \)**: First, we need to calculate \( 7^2 \):
\[ 7^2 = 49 \]

3. **Substitute \( 7^2 \) into the Equation**: Now substitute \( 49 \) back into the equation:
\[ 7(49) - 50(7) + k = 0 \]

4. **Calculate \( 7 \times 49 \)**: Now calculate \( 7 \times 49 \):
\[ 7 \times 49 = 343 \]

5. **Calculate \( 50 \times 7 \)**: Next, calculate \( 50 \times 7 \):
\[ 50 \times 7 = 350 \]

6. **Substitute the Values Back into the Equation**: Now substitute these values back into the equation:
\[ 343 - 350 + k = 0 \]

7. **Simplify the Equation**: Simplify the left-hand side:
\[ -7 + k = 0 \]

8. **Solve for \( k \)**: To find \( k \), add \( 7 \) to both sides:
\[ k = 7 \]

Thus, the value of \( k \) is \( 7 \).