8

Set 9: Quadratic Equations

Explanation

Answer: A

Determine the nature of the roots for 4x212x+9=04x^2 - 12x + 9 = 0.

A.

One real repeated root

✓ Correct
B.

Two distinct real roots

C.

No real roots

D.

One real and one imaginary

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Calculate the discriminant Δ=b24ac\Delta = b^2 - 4 ac. 1. Δ=(12)24(4)(9)\Delta = (-12)^2 - 4(4)(9). 2. Δ=144144=0\Delta = 144 - 144 = 0. 3. Since Δ=0\Delta = 0, there is exactly one real repeated root. Choice B is incorrect because Δ\Delta is not positive. Choice C is incorrect because Δ\Delta is not negative. Choice D is incorrect because roots come in conjugate pairs.

Key Steps:

The correct answer is One real repeated root

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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