Question

The single digit value of \( k \) satisfying the algebraic relation \( k + 1k + 2k + 4k + k^2 = 19k \), is:

• A. 7
• B. 6
• C. 5
• D. 4

Hint:

When solving quadratic equations, factorize them to find the roots. Always check for valid solutions within the given constraints.

Answer 1

The Correct Option is A

Step 1: Write the given equation: \[ k + 1k + 2k + 4k + k^2 = 19k \] Step 2: Combine like terms: \[ k + k + 2k + 4k + k^2 = 19k \quad \Rightarrow \quad 8k + k^2 = 19k \] Step 3: Simplify the equation: \[ k^2 + 8k - 19k = 0 \quad \Rightarrow \quad k^2 - 11k = 0 \] Step 4: Factor the quadratic equation: \[ k(k - 11) = 0 \] Step 5: Solve for \( k \): \[ k = 0 \quad \text{or} \quad k = 11 \] Step 6: Since the problem asks for the single digit value of \( k \), the valid solution is: \[ k = 7 \]