N nazfiz Member Joined Feb 3, 2010 Messages 121 Gender Male HSC 2013 Dec 28, 2011 #1 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!
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!
C cutemouse Account Closed Joined Apr 23, 2007 Messages 2,232 Gender Undisclosed HSC N/A Dec 28, 2011 #2 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.
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.
N nazfiz Member Joined Feb 3, 2010 Messages 121 Gender Male HSC 2013 Dec 28, 2011 #3 Oh okay, THANKS! I get it now
