If x2+4ax+2>0 for all values of x, then a lies in the interval:
-2,4
1,2
-2,2
-12,12
-4,2
Explanation for the correct option:
Solving the quadratic inequality:
In x2+4ax+2, we have a=1,b=4a,andc=2.
As x2+4ax+2>0, so b2-4ac<0.
⇒16a2-8<0⇒16a2<8⇒a-12a+12<0
So, -12<a<12
Hence, option D is correct.