If `2x^(3)+ax^(2)+bx+4=0` (a, b are positive real numbers) has 3 real roots then prove that `a+b ge 12 sqrt(2)`.

If 2x^3 +ax^2+ bx+ 4=0 (a and b are positive real numbers) has 3 real roots, then prove that a+ b ge 6 (2^(1/3)+ 4^(1/3))

If 2x^(3)+ax^(2)+bx+4=0 (a and b are positive real numbers) has three real roots. The minimum value of (a+b)^(3) is

If 2x^(3)+ax^(2)+bx+4=0 (a and b are positive real numbers) has three real roots. The minimum value of b^(3) is a. 108 b. 216 c. 432 d. 864

If 2x^(3)+ax^(2)+bx+4=0 (a and b are positive real numbers) has three real roots. The minimum value of a^(3) is a. 108 b. 216 c. 432 d. 864

If a,b,c are positive real numbers, then the number of real roots of the equation ax^2+b|x|+c is

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

If 16 x^(4) -32x ^(3) + ax ^(2) +bx + 1=0, a,b,in R has positive real roots only, then |b-a| is equal to :

If 16x^4-32x^3+ax^2+bx+1=0 , a,b in R has positive real roots only, then a-b is equal to :

If a,b,c are positive real numbers, then the number of positive real roots of the equation ax^(2)+bx+c=0 is

If c is positive and 2a x^2+3b x+5c=0 does not have any real roots, then prove that 2a-3b+5b>0.