Find the roots of the quadratic equation $6x^2 - x - 2 = 0$ using quadratic formula.
Step-by-Step Solution
Key Concept: $a = 6, b = -1, c = -2$. $D = 1 - 4(6)(-2) = 1 + 48 = 49$. $x = \dfrac{1 \pm 7}{12}$.
$D = (-1)^2 - 4(6)(-2) = 1 + 48 = 49$. [0.5 Mark]
$x = \dfrac{1 \pm 7}{12} \Rightarrow x = \dfrac{8}{12} = \dfrac{2}{3}$ or $x = \dfrac{-6}{12} = -\dfrac{1}{2}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Calculating $D = 49$: 0.5 Mark
Finding roots $2/3$ and $-1/2$: 1.5 Marks
Correct Answer: