All roots of the cubic `x^(3)+ax+b=0 (a,b in R)` are real and distinct, and `b>0` then

If all roots of the equation x^(3)+ax^(2)-ax-1=0 are real and distinct,then the set of values of a is

If the roots of the equation x^(2)+2ax+b=0 are real and distinct and they differ by at most 2m, then b lies in the interval

It roots of equation 2x^(2)+bx+c=0:b,c varepsilon R are real & distinct then the roots of equation 2cx^(2)+(b-4c)x+2c-b+1=0 are

If a and c are the lengths of segments of any focal chord of the parabola y^(2)=bx,(b>0) then the roots of the equation ax^(2)+bx+c=0 are real and distinct (b) real and equal imaginary (d) none of these

Prove that the roots of the quadratic equation ax^(2)-3bx-4a=0 are real and distinct for all real a and b,where a!=b.

If x^(2)-ax+b=0 where a,b in N has real and distinct roots,then a_(min)+b_(min)=

If the roots of equation ax^(2)+bx+c=0;(a,b,c in R and a!=0) are non-real and a+c>b. Then