Question

Find the set of values of a such that f(x) = x^3 - 3x +a has three real distinct roots....plz hlp..

Answer 1

here is an idea.
\[f'(x)=3x^2-3=3(x-1)(x+1)\]so we know the local max it at x = -1 and the local min is at x = 1. just make sure that local max is above x axis and local min is below.

Answer 2

\[f(-1)=2+a\]
\[f(1)=-2+a\]

Answer 3

tnx got it

Answer 4

k