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Quadratic Equations
RD Sharma
CBSE
Grade 10

Question:

Which of the following equations has two distinct real roots?
(a) $2x^2 - 3\sqrt{2} x + \dfrac{9}{4} = 0$
(b) $x^2 + x - 5 = 0$
(c) $x^2 + 3x + 2\sqrt{2} = 0$
(d) $5x^2 - 3x + 1 = 0$

Step-by-Step Solution

Key Concept: For $x^2 + x - 5 = 0$, $D = 1^2 - 4(1)(-5) = 1 + 20 = 21 > 0$.
For option 2: $D = 1 - 4(-5) = 21 > 0$, so it has two distinct real roots. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Calculating $D = 21 > 0$: 1.0 Mark

Correct Answer: $x^2 + x - 5 = 0$
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