Find the value of `k` if `x^3-3x+k=0` has three real distinct roots.

Find the value of a if x^3-3x+a=0 has three distinct real roots.

Find the value of a if x^3-3x+a=0 has three distinct real roots.

Find the value of k if 9x^2 + kx +1=0 has equal roots.

Draw the graph of f(x)=log_(e)(sqrt(1-x^(2))) .Find the range of the function .Also find the values of k if (k) has two distinct real roots.

Find the value of k for which the equation x^2 −6x+k=0 has distinct roots.

If a continuous function 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

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is three (b) two (c) infinitely many (d) zero

Minimum integral value of k for which the equation e^(x)=kx^(2) has exactly three real distinct solution,

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .