If equation `2x^(3)-6x+2sina+3=0,a in (0,pi)` has only one real root, then the largest interval in which a lies is

If the equation x^(2)-2ax+a^(2)+a-3=0 has exactly one real root in (1,3) then largest integral value of a is

Prove that the equation,3x^(3)-6x^(2)+6x+sin x=0 has exactly one real root.

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

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

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

Prove that the equation 3x^(5)+15x -8=0 has only one real root .

Show that the equation x^(3)+2x^(2)+x+5=0 has only one real root, such that [alpha]=-3 , where [x] denotes the integral point of x