Quadratic Equations Question - CBSE

Question

If $\dfrac{1}{2}$ is a root of the equation $x^2 + kx - \dfrac{5}{4} = 0$, then the value of $k$ is:
(a) $2$
(b) $-2$
(c) $\dfrac{1}{4}$
(d) $\dfrac{1}{2}$

Accepted Answer

\left(\dfrac{1}{2}\right)^2 + k\left(\dfrac{1}{2}\right) - \dfrac{5}{4} = 0 \Rightarrow \dfrac{1}{4} + \dfrac{k}{2} - \dfrac{5}{4} = 0$. [0.5 Mark]
\dfrac{k}{2} - 1 = 0 \Rightarrow \dfrac{k}{2} = 1 \Rightarrow k = 2. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Substituting $x = 1/2$: 0.5 Mark
Solving for $k = 2$: 0.5 Mark

Question:

Step-by-Step Solution

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