Question

The graphs of the two equations $y=a{x}^2+bx+c$ and $y=$ $A{x}^2+Bx+C$, such that $a$ and $A$ have different signs and that the quantities $b^2-4ac$ and $B^2-4AC$ are both negative,

• A. intersect at two points
• B. intersect at one point
• C. do not intersect
• D. none of the above

Answer 1

The correct option is C do not intersect

We have $y=a{x}^2+bx+c$ and $y=A{x}^2+Bx+c$

given that $a$ and $A$ have different sign.

Also $b^2=4ac<0$ and $B^2-4AC<0$

without loss of generality we can take $a>0$ and $A<0$

So let us draw graph.

Refer image.

Since one is below x-axis and other is above x-axis we have no intersection between both equation

Option (C)