Find the roots of $4x^2 + 4\sqrt{3} x + 3 = 0$ using quadratic formula.
Step-by-Step Solution
Key Concept: $D = (4\sqrt{3})^2 - 4(4)(3) = 48 - 48 = 0 \Rightarrow x = \dfrac{-4\sqrt{3}}{8} = -\dfrac{\sqrt{3}}{2}$.
$D = 48 - 48 = 0$. [0.5 Mark]
$x = \dfrac{-4\sqrt{3} \pm 0}{8} = -\dfrac{\sqrt{3}}{2}$. Roots are $-\dfrac{\sqrt{3}}{2}, -\dfrac{\sqrt{3}}{2}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Calculating $D = 0$: 0.5 Mark
Finding equal roots $-\sqrt{3}/2$: 1.5 Marks
Correct Answer: