Function f(x) has exactly one real root

[markosheehan]

f:x x³+(1-k²)x+k is a cubic function where k is a constant.1. show that -k is a root of f.2.find in terms of k the other two roots of f.3 find the set of values of k for which f has exactly one real root.

i think i know how to do the first question just sub in k for x and it should equal 0 but i dont know how to do the second and third qustion.

[Guest]

For 2 use polynomial long division to factor out the (x+k) factor.
https://en.wikipedia.org/wiki/Polynomial_long_division
This should leave a quadratic term which you can solve using the quadratic formula.

For 3 find the values of k such that the terms inside the square root part are negative.

Hope this helped,

R. Baber.