Conditions on a and b for which `x^2 -ax-b^2` is less than zero for at least one positive x are

Value (s) of 'a' for which ax^2+(a-3)x+1lt0 for at least one positive x.

Find all values of b for which x^(2)-x+b-3lt0 for at least one -vex.

If x is a real number than x^(2)+x+1 is (a) less than (3)/(4) (b) zero for at least one value of x (c) always negative (d) greater than or equal to (3)/(4)

Let f(x)=sqrt(ax^(2)+bx). Find the set of real values of 'a' for which there is at least one positive real value of 'b for which the domain of f and the range of f are the same set.

The set of exhaustive values of a for which the equation |ax-2|=2x^(2)+ax+4 has at least one positive root,is

The least integral value of a such that sqrt(9-a^(2)+2ax-x^(2)) > sqrt(16-x^(2)) for at least one positive x

The zero of p(x)=ax+b is

If p is a positive fraction less than 1, then (a) (1)/(p) is less than 1( b ) (1)/(p) is a positive integer (c) p^(2) is less than p(d)(2)/(p)-p is a positive number

If the equation ax^(2)+bx+c=0 has two positive and real roots,then prove that the eqsition ax^(2)+(b+6a)x+(c+3b)=0 has at least one positive real root.

If the roots of the equation x^(2)-ax+b=0y are real and differ b a quantity which is less than c(c>0), then show that b lies between (a^(2)-c^(2))/(4) and (a^(2))/(4)