SOLUTION: f(x) = x^3 + (1 - k^2)x + k (a) Show that -k is a root of f. I've already solved this by substituting -k to the x's in the given equation. I'm not sure tho. (b) Find, in ter

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: f(x) = x^3 + (1 - k^2)x + k (a) Show that -k is a root of f. I've already solved this by substituting -k to the x's in the given equation. I'm not sure tho. (b) Find, in ter      Log On


   

Question 815591: f(x) = x^3 + (1 - k^2)x + k
(a) Show that -k is a root of f.
I've already solved this by substituting -k to the x's in the given equation. I'm not sure tho.
(b) Find, in terms of k, the other roots of f.
what I did is:
let x + k a factor.
divide the equation x^3 + (1 - k^2)x + k by x + k
then I got x^2 + kx + 1
I then used quadratic formula to get the 2 other roots:
x = -k + or - square root of (k^2 - 4)
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(c)Find the set of values of k for which f has exactly one real root.
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Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Everything you've done is correct. All that is left is part c. A quadratic has exactly one real root when the expression inside the square root is a zero. So all you have to do is figure out when k%5E2-4 is zero.