(i) The positive value of k for which `ke^x-x=0` has only one root is

If a continous founction of defined on the real line R, assumes positive and negative values in R, then the equation f(x)=0 has a root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum values is negative, then the equation f(x)=0 has a root in R. Considetr f(x)=ke^(x)-x for all real x where k is real constant. The positive value of k for which ke^(x)-x=0 has only root is

If a continous founction of defined on the real line R, assumes positive and negative values in R, then the equation f(x)=0 has a root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum values is negative, then the equation f(x)=0 has a root in R. Considetr f(x)=ke^(x)-x for all real x where k is real constant. For k gt 0, the set of all values of k for which ke^(x)-x=0 has two distinct, roots, is

Find the least positive value of k for which the equation x^(2)+kx+4=0 has real roots.

Let us consider an equation f(x) = x^(3)-3x +k=0 .then the values of k for which the equation has Exactly one root which positive , then k belongs to

Let us consider an equation f(x) = x^(3)-3x +k=0 .then the values of k for which the equation has Exactly one root which is negative, then k belong

Find value of k if (k^(2)-1)x^(2)+4x+1=0 has one root =-1

Find the values of k for which 4x^(2)-2(k+1)x+(k+4)=0 has real and equal roots.

Find the value of k for which the equation 9x^(2)-24x+k=0 has equal roots.Also,find the roots.

Number of integral value (s) of k for which the equation 4x^(2)-16x+k=0 has one root lie between 1 and 2 and other root lies between 2 and 3, is