Math Is Fun Forum

helpplzquadsmath

Guest

What the heck is this even possible? quadratics

x[sup]4[/sup] - x[sup]3[/sup] + x - 1 = 0

I dunno how to start.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What the heck is this even possible? quadratics

Hi helpplzquadsmath;

If you are trying to solve for x then this one is not very difficult.

This is the simplest way but not the only way.

First graph the poly:

http://www.mathsisfun.com/graph/functio … =-8&ymax=8

Eyeball the 2 real roots. Plug in to the equation to confirm your guess. Call the two roots r1 and r2 respectively. Deflate the poly by dividing the poly by ( x - r1) and then by ( x - r2 ). You will be left with a quadratic, this you solve by the quadratic formula and you are done.

Or you can use the rational root theorem to find the 2 real roots. Or if you are good at factoring you could factor that polynomial. But the graphic way is the easiest.

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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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: What the heck is this even possible? quadratics

This factorisation jumped out at me:

(x-1)(x³+1) = 0

And from there it's fairly straightforward.
Bobby's method is good in general though. Sketch the graph, try to guess some roots, and use polynomial division to make finding the rest easier.

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Why did the vector cross the road?
It wanted to be normal.