Question

If $a,b,c$ are positive real numbers in geometric progression, then the graph of $y=a{x}^2+bx+c$ is a curve that

• A. Intersects the x-axis at two points
• B. Is entirely below the x-axis
• C. Is entirely above the x-axis
• D. Is tangent to the x-axis

Answer 1

The correct option is C Is entirely above the x-axis

Let

$a=a,b=ar,c=a{r}^2$

Then

$y=a{x}^2+arx+a{r}^2$

Discriminant $D=a^2{r}^2-4a^2{r}^2=-3a^2{r}^2$

Hence as D is negative y has complex roots and the graph lies above the x-axis entirely since coeffiecient of $x^2$ is positive