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Quadratic Equations
NCERT Exemplar
CBSE
Grade 10
Question:
The quadratic equation $2x^2 - \sqrt{5}x + 1 = 0$ has: (a) Two distinct real roots (b) Two equal real roots (c) No real roots (d) More than 2 real roots
Step-by-Step Solution
Key Concept: Compute discriminant $D = b^2 - 4ac$. If $D < 0$, there are no real roots.
Here $a=2, b=-\sqrt{5}, c=1$. $D = (-\sqrt{5})^2 - 4(2)(1) = 5 - 8 = -3$. [0.5 Mark] Since $D = -3 < 0$, the quadratic equation has no real roots. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Calculating $D = -3$: 0.5 Mark Deducing no real roots since $D < 0$: 0.5 Mark
Correct Answer:No real roots
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