Asked by bob
WHICH ONE DOESNβT BELONG? Use the discriminant to determine which of these equations is different from the others.
A. π₯2 β3β’π₯ β40 =0
B. 12β’π₯2 βπ₯ β6 =0
C. 12β’π₯2 +2β’π₯ β4 =0
D. 7β’π₯2 +6β’π₯ +2 =0
Equation 1 of 3.
Select Choice
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.
Select Choice
roots.
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Answered by
GPT-5 mini
AI
Answer: D
Compute discriminants D = b^2 β 4ac:
- A: 1Β·x^2 β 3x β 40 β D = (β3)^2 β 4(1)(β40) = 9 + 160 = 169 (>0) β 2 real roots.
- B: 12x^2 β x β 6 β D = (β1)^2 β 4(12)(β6) = 1 + 288 = 289 (>0) β 2 real roots.
- C: 12x^2 + 2x β 4 β D = 2^2 β 4(12)(β4) = 4 + 192 = 196 (>0) β 2 real roots.
- D: 7x^2 + 6x + 2 β D = 6^2 β 4(7)(2) = 36 β 56 = β20 (<0) β 2 complex (nonreal) roots.
Thus D is the one that doesnβt belong: it has two complex roots, while the other three have two real roots.
Compute discriminants D = b^2 β 4ac:
- A: 1Β·x^2 β 3x β 40 β D = (β3)^2 β 4(1)(β40) = 9 + 160 = 169 (>0) β 2 real roots.
- B: 12x^2 β x β 6 β D = (β1)^2 β 4(12)(β6) = 1 + 288 = 289 (>0) β 2 real roots.
- C: 12x^2 + 2x β 4 β D = 2^2 β 4(12)(β4) = 4 + 192 = 196 (>0) β 2 real roots.
- D: 7x^2 + 6x + 2 β D = 6^2 β 4(7)(2) = 36 β 56 = β20 (<0) β 2 complex (nonreal) roots.
Thus D is the one that doesnβt belong: it has two complex roots, while the other three have two real roots.
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