Find the value of the parameter $a$ for which the quadratic equation $2 x^{2} + (a - 4) x + (a - 2) = 0$ has one root equal to $2$ .

hard 4 marks Class 10 · Mathematics · Quadratic Equations

Answer

a =

\frac{2}{3}

The correct answer is a = $\frac{2}{3}$ — Hence the required value of the parameter is $a = \frac{2}{3}$ .

Step-by-step solution

If $x = 2$ is a root, it must satisfy the equation: $2 (2)^{2} + (a - 4) (2) + (a - 2) = 0$ .
Compute each term: $2 (4) = 8$ , $(a - 4) (2) = 2 a - 8$ , and $a - 2$ remains.
Write the sum: $8 + (2 a - 8) + (a - 2) = 0$ .
Combine like terms: $8 - 8 - 2 = - 2$ , and $2 a + a = 3 a$ .
Thus $3 a - 2 = 0$ .
Solve for $a$ : $3 a = 2 \Rightarrow a = \frac{2}{3}$ .
Hence the required value of the parameter is $a = \frac{2}{3}$ .

Common mistake: Substituting

x = 2

incorrectly, e.g., forgetting to multiply the coefficient

2

with

x^{2}

Concept tested: Using a known root to find a parameter

Published 22 August 2026 · Last updated 16 September 2026 · How this solution was prepared and checked