Question

WHICH ONE DOESN’T BELONG? Use the discriminant to determine which of these equations is different from the others.
A. 𝑥2 −3⁢𝑥 −40 =0

B. 12⁢𝑥2 −𝑥 −6 =0

C. 12⁢𝑥2 +2⁢𝑥 −4 =0

D. 7⁢𝑥2 +6⁢𝑥 +2 =0



Equation 1 of 3.
Select Choice
is different from the other 3 equations because it has 2 2 of 3.
Select Choice
roots, where the other 3 equations each have 2 irrational, complex, or rational roots?

Answer 1

Compute discriminants D = b^2 − 4ac:

A: a=1, b=−3, c=−40 → D = 9 − 4(1)(−40) = 169 (>0, perfect square) → two distinct rational real roots.

B: a=12, b=−1, c=−6 → D = 1 − 4(12)(−6) = 289 (>0, perfect square) → two distinct rational real roots.

C: a=12, b=2, c=−4 → D = 4 − 4(12)(−4) = 196 (>0, perfect square) → two distinct rational real roots.

D: a=7, b=6, c=2 → D = 36 − 4(7)(2) = −20 (<0) → two complex (nonreal) conjugate roots.

So choice D is different: it has two complex (nonreal) roots, while A, B, and C each have two real rational roots.