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algebra

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.
Original post by 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.


1. if -k is a root, then f(-k)=0,

2 Since -k is a root, then "x-(-k)", i.e. (x+k) will be a factor. So, polynomial/long division to get the other factor which will be a quadratic.
i am trying to divide x^3+(1-k^2)x+k by (x+k) but i cant do this can you show me how to.
Original post by markosheehan
i am trying to divide x^3+(1-k^2)x+k by (x+k) but i cant do this can you show me how to.


If you're having problems it may help to write x^3+(1-k^2)x+k as x^3+ 0x^2 + (1-k^2)x+k

I'll write and scan it if you're still stuck, but I'd rather not.
(edited 7 years ago)

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