Urgent! Two exercises of roots for 2 polynoms ...

May 2012
92
5
slovenia
Hey, guys!

I have 2 exercises, which I don't know how to solve it without Wolframalpha.

1. Find all \(\displaystyle \mathbb{R}\) solutions of equation: \(\displaystyle 4x^4 + 4x^3 - 11x^2 - 6x + 8 = 0\).

2. Find all \(\displaystyle \mathbb{R}\) solutions of equation: \(\displaystyle x^4 - 4x^3 + 6x^2 - 4x - 3 = 0\).

I tried with formulas \(\displaystyle 4(x - A)(x - B)(x - C)(x - D)\) and \(\displaystyle (x^2 + Ax + B)(x^2 + Cx + D)\), but I couldn't figure out the solutions. Can somebody explain me how to find solutions of these 2 exercises? [:D]
 
Last edited:

Plato

MHF Helper
Aug 2006
22,489
8,652
Hey, guys!

I have 2 exercises, which I don't know how to solve it without Wolframalpha.

1. Find all \(\displaystyle \mathbb{R}\) solutions of equation: \(\displaystyle 4x^4 + 4x^3 - 11x^2 - 6x + 8 = 0\).

2. Find all \(\displaystyle \mathbb{R}\) solutions of equation: \(\displaystyle x^4 - 4x^3 + 6x^2 - 4x - 3 = 0\).

I tried with formulas \(\displaystyle 4(x - A)(x - B)(x - C)(x - D)\) and \(\displaystyle (x^2 + Ax + B)(x^2 + Cx + D)\), but I couldn't figure out the solutions. Can somebody explain me how to find solutions of these 2 exercises? [:D]
\(\displaystyle \begin{align*} x^4 - 4x^3 + 6&x^2 - 4x - 3\\(x-1)^4&-4\\\left[(x-1)^2+2\right]&\left[(x-1)^2-2\right]\\\left(x^2-2x+3\right)&\left(x^2-2x-1\right) \end{align*}\)

Use the quadratic equation twice.
 
Last edited:
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May 2012
92
5
slovenia
Wow! Ok, thank you for this solution. ;) Sorry to update so late.
 
Dec 2013
2,002
757
Colombia
I think the first was supposed to be \(\displaystyle 4x^4+4x^3-11x^2-8x+6\) which factorises nicely.
 
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