What are the solutions to the equation 2x^5+24x=14x^3 ?

The solutions to the equation 2x^5+24x=14x^3 are x=0,x=-sqrt(3),x=sqrt(3),x=-2,x=2

Find the zeros of 2x^5+24x=14x^3

The zeros of 2x^5+24x=14x^3 are x=0,x=-sqrt(3),x=sqrt(3),x=-2,x=2

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2 x^{5} + 24 x = 14 x^{3}

x = 0, x = - 3, x = 3, x = - 2, x = 2

Decimal Notation

x = 0, x = - 1.73205 \dots, x = 1.73205 \dots, x = - 2, x = 2

Solution steps

2 x^{5} + 24 x = 14 x^{3}

Move

14 x^{3}

to the left side

2 x^{5} + 24 x - 14 x^{3} = 0

Factor

2 x^{5} + 24 x - 14 x^{3} : 2 x (x + 3) (x - 3) (x + 2) (x - 2)

2 x (x + 3) (x - 3) (x + 2) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 3 = 0 or x - 3 = 0 or x + 2 = 0 or x - 2 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = 0, x = - 3, x = 3, x = - 2, x = 2

\frac{1}{2} = 4 x^{3} - 9 x^{2} - 1

x^{3} + 9 x^{2} + 20 x = 0

x^{3} - 8 x^{2} + 5 x + 14 = 0

2 x^{4} - 2 = 0

x^{4}

What are the solutions to the equation 2x^5+24x=14x^3 ?
The solutions to the equation 2x^5+24x=14x^3 are x=0,x=-sqrt(3),x=sqrt(3),x=-2,x=2
Find the zeros of 2x^5+24x=14x^3
The zeros of 2x^5+24x=14x^3 are x=0,x=-sqrt(3),x=sqrt(3),x=-2,x=2