poly (1 Viewer)

[fullonoob]

Solve the equation x^4 + 4x^3 + 5x^2 + 2x - 20 = 0

If the equation x^3 + 3px + q = 0 has double root for p< 0 and q>0, prove that q^2 + 4p^3 = 0

many thanks

 

[buchanan]

So or

For the other one, the double root will be a root of the derivative, so and .

So



So

 

[fullonoob]

So or

For the other one, the double root will be a root of the derivative, so and .

So



So

thx but for the first one how'd you know it = (x^2+2x-4)(x^2+2x+5)=0 on the first step??

 

[buchanan]

You could do a substitution.

Let

So

Hence

 

[buchanan]

It's a bit boring though.

See if you can solve exactly.

(The 1969 3 unit paper asked for the approximate solution to this using Newton's method, but you can actually solve it exactly.)

 

[fullonoob]

It's a bit boring though.

See if you can solve exactly.

(The 1969 3 unit paper asked for the approximate solution to this using Newton's method, but you can actually solve it exactly.)

answer that one please xDD

 

[xV1P3R]

It's a bit boring though.

See if you can solve exactly.

(The 1969 3 unit paper asked for the approximate solution to this using Newton's method, but you can actually solve it exactly.)

I too would like to know!

 

[buchanan]

I started a thread on this stuff a few years ago at <a href="http://community.boredofstudies.org/238/extracurricular-topics/99063/cubics-quartics.html">http://community.boredofstudies.org/238/extracurricular-topics/99063/cubics-quartics.html</a> , and that was one of the questions in that thread.

The answer (for real x) is

I used the quartic formula

http://users.tpg.com.au/nanahcub/quartic.gif

This also requires the use of the cubic formula to solve a resolvent cubic first:

http://users.tpg.com.au/nanahcub/cubic.gif

 

[buchanan]

Somewhat uglier, but equivalent expressions from wolframalpha.com yield the four roots, the last two of which are the complex roots:

 

[adomad]

Somewhat uglier, but equivalent expressions from wolframalpha.com yield the four roots, the last two of which are the complex roots:

have you tried getting a Girl friend to fill in your spare time?

 

[buchanan]

Solve the equation x^4 + 4x^3 + 5x^2 + 2x - 20 = 0

Now we can go back to fullonoob's question, modify it a bit and get more interesting ones by just removing some terms. This actually makes the question much harder and much more interesting:

Solve

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

(and of course there are others, but they are too boring)

 

[fullonoob]

wtf is this O_O
has it been removed from the new syllabus?
never encountered any such question
i dont even really wna read the working out cos its so long xD