1

Set 1: Quadratic Equations

Explanation

Answer: B

How many real solutions: x24x+4=0x^2 - 4x + 4 = 0?

A.

0

B.

1

✓ Correct
C.

2

D.

3

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Discriminant: Δ=1616=0\Delta = 16 - 16 = 0. When Δ=0\Delta = 0, there's exactly one repeated real solution. Factor: x24x+4=(x2)2=0x^2 - 4 x + 4 = (x - 2)^2 = 0, so x=2x = 2 (repeated). Choice A is incorrect because Δ=0\Delta = 0 means one solution exists. Choice C is incorrect because two distinct solutions require Δ>0\Delta > 0. Choice D is incorrect because quadratics never have three solutions.

Key Steps:

The correct answer is 1

Why others are wrong:
A: Choice A 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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