Question

If f(x) = ax2 + bx + c, where a, b, c ∈ R and a < 0, such that ax2 + bx + c = 0 does not have any real roots then

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.

Answer 2

my self shreya,,,,,

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