What is the value of k?

Question

Find the value of k if #x^3 - 3x + a = 0# has three real distinct roots

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Answer 1 · 2018-07-20T21:19:47

If #a = k#, then #-2 < k < 2#

Given: #x^3 - 3x + a = 0#

The top graph is #x^3 - 3x + 2 = 0 " "=>" "# only has two real roots.

The bottom graph is #x^3 - 3x + 2 = 0 " "=>" "# only has two real roots.

This means if #a = k#, then #-2 < k < 2#
graph{(y - x^3 + 3x - 2) (y - x^3 +3x + 2)= 0 [-10, 10, -5, 5]}

Graph when #a = 1#:
graph{x^3 - 3x + 1 [-10, 10, -5, 5]}