not sure what they are talking about??

Question

find the rational roots of f. list any irrational roots correct to two decimal places
f(x)= x^4-2x^3-10x^2+14x+21

I haven't learned this yet so I am not sure how to begin or what I am looking for

that is what I am asking for is for someone to show me..........this kind of problem may be on the finals I have to take in two days.

please, if you can't help don't reply

Answer 1

How to begin?

Learn it first.

Answer 2

First of all, you should know that if you substitute a number

into f[x], and the result is zero, then you have a factor of f[x].

Because the constant is 21, whose factors are 1,3 and 7,

I tried first f[1], no luck, and then f[-1], which gave f[-1]=0,

so, giving [x+1] as a factor.I then divided f[x] by x+1,giving

x^3 -3x^2-7x+21, which I will now call g[x]. The constant is 21,

so for the same reasons as before, I tried g[3], which =0. So

[x-3] is a factor. I then divided g[x] by x-3, giving x^2-7, which

you may recognise as the difference of two squares. so, f[x]

factorises to:[x+1][x-3][x+rt7][x-rt7]. the two irrational roots

positive root 7, and negative root7, you will have to find

yourself, I have no calculator.I have assumed a lot here, that

you can do long algebraic division, an you follow the method

of finding factors by inspection. hope it helps, Twiggy.