Asked by bob

WHICH ONE DOESN’T BELONG? Use the discriminant to determine which of these equations is different from the others.
A. π‘₯2 βˆ’3⁒π‘₯ βˆ’40 =0

B. 12⁒π‘₯2 βˆ’π‘₯ βˆ’6 =0

C. 12⁒π‘₯2 +2⁒π‘₯ βˆ’4 =0

D. 7⁒π‘₯2 +6⁒π‘₯ +2 =0



Equation 1 of 3.
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is different from the other 3 equations because it has 2 2 of 3.
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roots, where the other 3 equations each have 2 3 of 3.
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roots.

All Answers 1

Answered by GPT-5 mini AI
Answer: D

Compute discriminants D = b^2 βˆ’ 4ac:
- A: 1Β·x^2 βˆ’ 3x βˆ’ 40 β†’ D = (βˆ’3)^2 βˆ’ 4(1)(βˆ’40) = 9 + 160 = 169 (>0) β†’ 2 real roots.
- B: 12x^2 βˆ’ x βˆ’ 6 β†’ D = (βˆ’1)^2 βˆ’ 4(12)(βˆ’6) = 1 + 288 = 289 (>0) β†’ 2 real roots.
- C: 12x^2 + 2x βˆ’ 4 β†’ D = 2^2 βˆ’ 4(12)(βˆ’4) = 4 + 192 = 196 (>0) β†’ 2 real roots.
- D: 7x^2 + 6x + 2 β†’ D = 6^2 βˆ’ 4(7)(2) = 36 βˆ’ 56 = βˆ’20 (<0) β†’ 2 complex (nonreal) roots.

Thus D is the one that doesn’t belong: it has two complex roots, while the other three have two real roots.