Question

15. If f(x) = ax2 - x + c such that ac > 1 and its graph lies below the x-axis, then
(1) a < 0, c> 0
(2) a < 0, < 0
(3) a > 0, C> 0
(4) a > 0, c < 0
[ans given 2. plz solve with explanation]​

Answer 1

Answer:

Consider the equation,

ax

2

+bx+c

Now if b

2

−4ac<0, then it does not have any real roots and hence it will not intersect the x axis at any point.

If a>0 then y=ax

2

+bx+c will lie completely above x axis and

If a<0 then y=ax

2

+bx+c will lie completely below x axis.

It is given that the above equation is always greater than zero,

Or

ax

2

+bx+c>0 for ϵR.

This can only occur is

b

2

−4ac<0 and a>0