If $x = 4$ is a root of the equation $x^{2} - k x + 12 = 0$ , find the value of $k$ .

hard MCQ 4 marks Class 6 · Mathematics · Algebra

Answer

The correct answer is 7 — Divide both sides by $- 4$ to solve for $k$ : $k = \frac{- 28}{- 4} = 7$ . Dividing by a negative number flips the sign, giving the correct integer value.

Step-by-step solution

Substitute $x = 4$ into the equation: $4^{2} - 4 k + 12 = 0$ . This replaces the variable with its known value to find $k$ .
Compute the squares and constants: $16 - 4 k + 12 = 0$ simplifies to $28 - 4 k = 0$ because $16 + 12 = 28$ .
Move the constant term to the other side: $- 4 k = - 28$ . This isolates the term containing $k$ on one side.
Divide both sides by $- 4$ to solve for $k$ : $k = \frac{- 28}{- 4} = 7$ . Dividing by a negative number flips the sign, giving the correct integer value.

Common mistake: Altering the sign of the constant term when moving it across the equation

Concept tested: Using a known root to find missing coefficient

Published 7 October 2026 · How this solution was prepared and checked

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If x=4 is a root of the equation x2−kx+12=0, find the value of k.

Step-by-step solution

If $x = 4$ is a root of the equation $x^{2} - k x + 12 = 0$ , find the value of $k$ .