Quadratic Equations
NCERT Exemplar Ch 04
CBSE_NCERT_EXEMPLAR_CH04
Grade 10
Question:
If $\dfrac{1}{2}$ is a root of the equation $x^2 + kx - \dfrac{5}{4} = 0$, then the value of $k$ is:
$2$
$-2$
$\dfrac{1}{4}$
$\dfrac{1}{2}$
Step-by-Step Solution
Key Concept: Substitute $x = 1/2$ into the quadratic equation.
Stepwise Solution:
\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]
Marking Scheme:
• Substituting $x = 1/2$: 0.5 Mark
• Solving for $k = 2$: 0.5 Mark
Correct Answer: $2$
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