2

Set 4: Quadratic Equations (Intermediate)

Explanation

Answer: A

A student solved 2x24x3=02x^2 - 4x - 3 = 0 and got x=4±402x = \frac{4 \pm \sqrt{40}}{2}. What error did they make?

A.

Wrong denominator

✓ Correct
B.

Wrong sign for b

C.

Wrong discriminant calculation

D.

No error

Detailed Explanation

Choice A is correct. Choice A is the correct answer. The quadratic formula is x=b±Δ2ax = \frac{-b \pm \sqrt{\Delta}}{2 a}. * Here a=2a=2, so the denominator should be 2(2)=42(2) = 4. * The student used 2, likely forgetting to multiply by aa. Choice B is incorrect because (4)=4-(-4) = 4 is correct. Choice C is incorrect because Δ=(4)24(2)(3)=16+24=40\Delta = (-4)^2 - 4(2)(-3) = 16 + 24 = 40 is correct. Choice D is incorrect because the denominator is definitely wrong.

Key Steps:

The correct answer is Wrong denominator

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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