Geometric series question (1 Viewer)

[nazfiz]

a,b and c are positive, consecutive terms of a geometric series. Show that the graph for y= ax^2+ bx+c is entirely above the x-axis.

Thanks!

 

[cutemouse]

As a, b, c are in GP: b = ar, c = ar^2 for some r>0 (as b, c > 0)

Now as a>0

and Δ=b^2 - 4ac = (ar)^2 - 4a(ar^2) = -3(ar)^2 < 0 (as (ar)^2 >0)

Therefore y=ax^2+bx+c is positive definite and therefore lies entirely above the x axis.

 

[nazfiz]

Oh okay, THANKS!
I get it now