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What are the solution(s) of the equation?
- 5x4 + 16x? + 32x= - 6x4 - 2x3

User Mario Awad
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1 Answer

2 votes

Answer:

The solutions are:

x=0, x=-2, x=4i, x=-4i

Explanation:

We need to find solutions of the equation
- 5x^4 + 16x^2 + 32x= - 6x^4 - 2x^3

Note in given question:
- 5x^4 + 16x? + 32x= - 6x^4 - 2x^3 considering 2 instead of ?

Solving:


- 5x^4 + 16x^2 + 32x= - 6x^4 - 2x^3


- 5x^4 + 16x^2 + 32x+ 6x^4 + 2x^3=0\\- 5x^4+ 6x^4 + 16x^2 + 32x + 2x^3=0\\x^4+2x^3+16x^2+32x=0Taking x common


x(x^3+2x^2+16x+32)=0\\x=0 \ or \ x^3+2x^2+16x+32=0


Simplifying \ x^3+2x^2+16x+32=0 \ we \ get (x+2)(x^2+16)


x=0 \ or \ (x+2)(x^2+16)=0\\x=0 \ or \ x+2=0 \ or x^2+16=0\\x=0 \ or \ x=-2 \ or x^2=-16\\We \ know \ √(-1)=i \\x=0 \ or \ x=-2 \ or x=\pm 4i\\

So, the solutions are:

x=0, x=-2, x=4i, x=-4i

User Tshalif
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