The number of value of k for which the equation x3 – 3x + k = 0 has two different roots lying in the interval (0, 1) are
Answer & explanation
Correct answer: option 4
Let f(x) = x3 – 3x + k
f'(x) = 3(x – 1) (x + 1)
Thus the stationary points being +1 and −1 they lie outside the given region hence no value of k can make the equation roots lie in the given range of (0,1).