What are the solutions to the equation x^4-21x^2+80=0 ?

The solutions to the equation x^4-21x^2+80=0 are x=4,x=-4,x=sqrt(5),x=-sqrt(5)

Find the zeros of x^4-21x^2+80=0

The zeros of x^4-21x^2+80=0 are x=4,x=-4,x=sqrt(5),x=-sqrt(5)

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x^{4} - 21 x^{2} + 80 = 0

x = 4, x = - 4, x = 5, x = - 5

Decimal Notation

x = 4, x = - 4, x = 2.23606 \dots, x = - 2.23606 \dots

Solution steps

x^{4} - 21 x^{2} + 80 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 21 u + 80 = 0

Solve

u^{2} - 21 u + 80 = 0 : u = 16, u = 5

u = 16, u = 5

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 16 : x = 4, x = - 4

Solve

x^{2} = 5 : x = 5, x = - 5

The solutions are

x = 4, x = - 4, x = 5, x = - 5

(\frac{4 x - 7}{3})^{3} = 27

x^{3} + 5 x^{2} = - 6 x

x, x^{3} - 2 x^{2} - 5 x + 6 = 0

2 x^{3} - 7 x^{2} + 32 x - 112 = 0

F, t = (F^{3} + G) a

What are the solutions to the equation x^4-21x^2+80=0 ?
The solutions to the equation x^4-21x^2+80=0 are x=4,x=-4,x=sqrt(5),x=-sqrt(5)
Find the zeros of x^4-21x^2+80=0
The zeros of x^4-21x^2+80=0 are x=4,x=-4,x=sqrt(5),x=-sqrt(5)