Math Is Fun Forum

markosheehan

Member

Registered: 2016-06-15

Posts: 51

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: algebra

Hi;

1)

Substitute -k for x.

Simplify that.

2)

Deflate out the root x = -k by dividing x^3+(1-k^2)x+k by x + k. You will get the quadratic,

This you should be able to solve using the quadratic formula.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

markosheehan

Member

Registered: 2016-06-15

Posts: 51

Re: algebra

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: algebra

hi markosheehan

Welcome to the forum.

I think you'll always find this type of 'division' tricky unless you can do 'long division' with ordinary arithmetic first.  How are you with long division?  eg 3266 ÷ 23

If the answer is 'not so good' then it'll be worth looking at that first.  The rules of algebra are just the same as the rules of arithmetic, so it's worth making sure of that first.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: algebra

Hi;

Sorry, I assumed that anyone being asked that type of root question had been first shown how to divide two polynomials. Answer Bob's question and if that is easy then we can go over polynomial division. Maybe you can tell what type and how much math you already know.

Here is a good page on polynomial division.

http://www.mathsisfun.com/algebra/polyn … -long.html

If you know how to solve sets of simultaneous equations we can get the answer without having to divide polynomials.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: algebra

The way question is asked you have to substitute x=-k and show the expression is 0. But alternately

Last edited by thickhead (2016-06-16 21:33:44)

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