What are the solutions to the equation x^4-12x^2+20=0 ?

The solutions to the equation x^4-12x^2+20=0 are x=sqrt(10),x=-sqrt(10),x=sqrt(2),x=-sqrt(2)

Find the zeros of x^4-12x^2+20=0

The zeros of x^4-12x^2+20=0 are x=sqrt(10),x=-sqrt(10),x=sqrt(2),x=-sqrt(2)

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x^{4} - 12 x^{2} + 20 = 0

x = 10, x = - 10, x = 2, x = - 2

Decimal Notation

x = 3.16227 \dots, x = - 3.16227 \dots, x = 1.41421 \dots, x = - 1.41421 \dots

Solution steps

x^{4} - 12 x^{2} + 20 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 12 u + 20 = 0

Solve

u^{2} - 12 u + 20 = 0 : u = 10, u = 2

u = 10, u = 2

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 10 : x = 10, x = - 10

Solve

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

The solutions are

x = 10, x = - 10, x = 2, x = - 2

x^{3} - 4 x^{2} + 8 = 0

x^{3} + 5 x^{2} + 2 x + 10 = 0

- x (6 x + 7) (x^{2} - 36) = 0

x^{5} + 125 x^{2} = 0

0 = 4 x^{4} - 17 x^{2} + 4

What are the solutions to the equation x^4-12x^2+20=0 ?
The solutions to the equation x^4-12x^2+20=0 are x=sqrt(10),x=-sqrt(10),x=sqrt(2),x=-sqrt(2)
Find the zeros of x^4-12x^2+20=0
The zeros of x^4-12x^2+20=0 are x=sqrt(10),x=-sqrt(10),x=sqrt(2),x=-sqrt(2)