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

### Step 1: Substitute the root into the equation
Since we know that \( x = 7 \) is a root of the equation, we can substitute \( x \) with 7 in the equation:

\[ k(7^2) - 50(7) + k = 0 \]

### Step 2: Simplify the equation
Calculating \( 7^2 \):

\[ k(49) - 50(7) + k = 0 \]

Calculating \( 50 \times 7 \):

\[ 49k - 350 + k = 0 \]

### Step 3: Combine like terms
Now, combine the \( k \) terms:

\[ 49k + k - 350 = 0 \]

This simplifies to:

\[ 50k - 350 = 0 \]

### Step 4: Solve for \( k \)
Now, isolate \( k \) by adding 350 to both sides:

\[ 50k = 350 \]

Next, divide both sides by 50:

\[ k = \frac{350}{50} \]

Calculating the division:

\[ k = 7 \]

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

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