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

If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real roots, then the smallest integral value of |k| is:

If the equation x^(3)-6x^(2)+9x+lambda=0 has exactly one root in (1, 3), then lambda belongs to the interval

Prove that the equation x^(3) + x – 1 = 0 has exactly one real root.

If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solution for x, then possible integral value of a is:

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

If roots of the equation x^(2)-2ax+a^(2)+a-3=0 are real and less than 3 then a)a 4

If the equation x^(4)+ax^(3)+2x^(2)+bx+1=0 has at least one real root (a ,b in R) then the minimum value of a^(2)+b^(2)

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 .

If the equation ax^(2) + 2 bx - 3c = 0 has no real roots and (3c)/(4) lt a + b , then