2

Set 7: Quadratic Equations (Intermediate)

Explanation

Answer: A

Calculate the discriminant (b24acb^2 - 4ac) for x2+4x+4=0x^2 + 4x + 4 = 0.

A.

0

✓ Correct
B.

16

C.

32

D.

-16

Detailed Explanation

Choice A is correct. Choice A is the correct answer. The discriminant formula is Δ=b24ac\Delta = b^2 - 4 ac. 1. Identify coefficients: a=1,b=4,c=4a=1, b=4, c=4. 2. Substitute: Δ=424(1)(4)\Delta = 4^2 - 4(1)(4). 3. Calculate: 1616=016- 16 = 0. A discriminant of 0 indicates that the quadratic has exactly one real solution (a repeated root). Choice B is incorrect because it calculates b2b^2 only. Choice C is incorrect because it adds 4ac4ac instead of subtracting (16+1616 +16). Choice D is incorrect because it subtracts in reverse order (4acb24ac - b^2).

Key Steps:

The correct answer is 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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