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

#### lebdim

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? []

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MHF Helper
1 person

#### Plato

MHF Helper
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? []
\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*}

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3 people

#### lebdim

Wow! Ok, thank you for this solution. Sorry to update so late.

#### Archie

I think the first was supposed to be $$\displaystyle 4x^4+4x^3-11x^2-8x+6$$ which factorises nicely.

1 person