is b^2 + 2ab - 48a^2 0 ?

Question

Is  b^2 + 2ab -48a^2 >0  ?

1.  ax^2+bx+4a>0 , for every real x
2.  2ax^2 +( \sqrt{4b} )x+3=0, for only one real x

DimasSpb · Answer

I think that answer is D

Explanation:
Second statement tell us that 4b - 24a must be equal 0 because of one route of equation. 
SO 24a=4b and 6a = b
Replace letters in stem:  36a^2 + 12a^2 - 48a^2  = 0, so answer is NO. B - sufficient

First statement
Lets try play with numbers
For example that x=1, so equation will be b+5a>0 => b>-5a
Replace letters in stem:  25a^2 -10a^2 -48a^2 = -32a^2>0 ? Answer is NO
x=2
4a+2b +4a >0 => b>-4a
 16a^2 - 8a^2 - 48a^2 = -40a^2 >0 ? Answer is NO
x=3
9a +3b +4a >0 => b>  - \frac{13a}{3} 
 \frac{169a^2}{9} - \frac{26a^2}{3} -48a^2 . Again answer in NO

akansal211 · Answer

Can someone explain how statement 1 is sufficient?

nick1816 · Answer

b^2 + 2ab -48a^2 >0 or (b-6a)(b+8a)>0 Statement 1- ax^2+bx+4a>0 If this is true for all values of x. then a>0 and Discriminant<0 b^2-16a^2<0 (b-4a) (b+4a)<0 (b-4a)<0 and b+4a>0 or we can say b-6a<0 and b+8a>0 Hence (b-6a)(b+8a)<0 Sufficient

is b^2 + 2ab - 48a^2 > 0 ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards