Set 1: Quadratic Equations (Intermediate)

Explanation

Answer: A

Which equation has two distinct real roots?

$x^2 + 2x - 1 = 0$

✓ Correct

$x^2 + 2x + 1 = 0$

$x^2 + x + 1 = 0$

$x^2 + 5 = 0$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. We need $\Delta > 0$ . * A: $2^2 - 4(1)(-1) = 4 + 4 = 8$ . ( $8> 0$ , Two roots). * B: $2^2 - 4(1)(1) = 4 - 4 = 0$ . (One root). * C: $1^2 - 4(1)(1) = 1 - 4 = -3$ . (No real roots). * D: $0^2 - 4(1)(5) = -20$ . (No real roots). Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $x^2 + 2x - 1 = 0$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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