​​PLEASE ANSWER CORRECTLY
​​PLEASE ANSWER CORRECTLY The number of values of k for which the equation x3-3x+k=0 has two different roots lying in the interval (0, 1) are infinitely many no value of k satisfies the requirement.

Dear student,

We have,fx=x3-3x+kf'x=3x2-3But, f'x=03x2-3=0x2=33=1x=+1, -1the condition of two distinct root is fα×fβ=0     where α and β are roots of f'x=0f1×f-1=13-3×1+k×-13-3×-1+k=01-3+k×-1+3+k=0k-2×k+2=0k=2,-2thus k-2,-1,0,1,2-2thus the number of value of k in 0,1 is 0,1 itself i.e, 2Hence option 2 is correct
Regards

  • -2
What are you looking for?