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Find all zeros: x^5-6x^3+5x

User BLaminack
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1 Answer

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Answer:

On simplifing the given equation we get,


x^5-6x^3+5x
x(x^4-6x^2+5)

To find the zeros of the equation, consider


x(x^4-6x^2+5)=0

we get, x=0 or,


x^4-6x^2+5=0

When x=1, we get 1-6+1=5-5=0

Hence x=1 is the zero of the above equation,

To find the factors, we use L division method

we get,


x^4+0x^3-6x^2+0x+5=0

The coefficients of x power in decreasing order is 1,0,-6,0,5

we get,


\begin{gathered} x^4-6x^2+5=0 \\ (x-1)(x^3+x^2-5x-5)=0 \end{gathered}

x=1 or,


x^3+x^2-5x-5=0

When x=-1, we get -1+1+5-5=0

Hence x=-1 is the zero of the equation.

To find the factors, we use L division method

we get,

we get,


\begin{gathered} x^3+x^2-5x-5=0 \\ (x+1)(x^2-5)=0 \end{gathered}

we get, x=-1 or,


\begin{gathered} x^2-5=0 \\ x^2=5 \end{gathered}
x=\sqrt[]{5}\text{ or }x=-\sqrt[]{5}

The zeros of the given equation are,


x=0,1,-1,\sqrt[]{5},-\sqrt[]{5}

Find all zeros: x^5-6x^3+5x-example-1
Find all zeros: x^5-6x^3+5x-example-2
User BananaNeil
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