- #1
Saitama
- 4,243
- 93
Problem:
If the curve $y=ax^2+2bx+c$, ($a,b,c \,\in\,\mathbb{R},\,a,b,c \neq 0$) never meet the x-axis, then a,b,c can't be in
A)Arithmetic Progression
B)Geometric Progression
C)Harmonic Progression
D)All of these
Attempt:
Since, the curve never meets the x-axis, we have the condition that the discriminant of the quadratic is less than zero, hence,
$$b^2<ac$$
The above shows that a,b,c can't be in geometric progression. But the given answers are A and B, how do I show that they are not in arithmetic progression?
Any help is appreciated. Thanks!
If the curve $y=ax^2+2bx+c$, ($a,b,c \,\in\,\mathbb{R},\,a,b,c \neq 0$) never meet the x-axis, then a,b,c can't be in
A)Arithmetic Progression
B)Geometric Progression
C)Harmonic Progression
D)All of these
Attempt:
Since, the curve never meets the x-axis, we have the condition that the discriminant of the quadratic is less than zero, hence,
$$b^2<ac$$
The above shows that a,b,c can't be in geometric progression. But the given answers are A and B, how do I show that they are not in arithmetic progression?
Any help is appreciated. Thanks!