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Monday, November 08, 2010
DS - Quadratic, Parabola, and Inequalities
In xy-plane, Y = ax^2 + bx + c, does the graph intersect with X axis? 1) a > 0 2) c < 0
It will intersect X axis when Y = 0...ie. ax^2+bx+c = 0...has real roots... ie discriminant > 0 b^2 - 4ac >= o b^2 >= 4ac
Use (1): If a > 0, RHS depends on c.. Use (2): If c < 0, RHS depends on a... Combine both.. a>0 and c <0..so ac < 0 Since square of a number is always > 0...we can say that b^2 > 4ac.. Ans is C
1 comments:
It will intersect X axis when Y = 0...ie. ax^2+bx+c = 0...has real roots...
ie discriminant > 0
b^2 - 4ac >= o
b^2 >= 4ac
Use (1):
If a > 0, RHS depends on c..
Use (2):
If c < 0, RHS depends on a...
Combine both..
a>0 and c <0..so ac < 0
Since square of a number is always > 0...we can say that b^2 > 4ac..
Ans is C
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