U10 (e) Solve the equation 2x4 + 5x3 – 5x

asked May 1, 2023 72.5k views

16 votes

U10 (e) Solve the equation 2x4 + 5x3 – 5x – 2 = 0

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6 votes

Answer:

x₁=1; x₂=-1; x₃=-0.5; x₄=-2.

Explanation:

$2x^4+5x^3-5x-2=0; \ < = > \ 2(x^4-1)+5x(x^2-1)=0; \ < = > \ 2(x^2+1)(x^2-1)+5x(x^2-1)=0; \ < = >$

$(x^2-1)(2x^2+2+5x)=0; \ < = > \ (x^2-1)(2x^2+5x+2)=0; \ = >$

$= > \ \left[\begin{array}{ccc}x=1\\x=-1\\x=-(1)/(2) \\x=-2\end{array}$

Sebo answered May 5, 2023