What are the solutions to the equation x^4-13x^2+40=0 ?

The solutions to the equation x^4-13x^2+40=0 are x=2sqrt(2),x=-2sqrt(2),x=sqrt(5),x=-sqrt(5)

Find the zeros of x^4-13x^2+40=0

The zeros of x^4-13x^2+40=0 are x=2sqrt(2),x=-2sqrt(2),x=sqrt(5),x=-sqrt(5)

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x^{4} - 13 x^{2} + 40 = 0

x = 22, x = - 22, x = 5, x = - 5

Decimal Notation

x = 2.82842 \dots, x = - 2.82842 \dots, x = 2.23606 \dots, x = - 2.23606 \dots

Solution steps

x^{4} - 13 x^{2} + 40 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 13 u + 40 = 0

Solve

u^{2} - 13 u + 40 = 0 : u = 8, u = 5

u = 8, u = 5

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 8 : x = 22, x = - 22

Solve

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

The solutions are

x = 22, x = - 22, x = 5, x = - 5

x, y^{2} = x^{3}

z^{5} = - 163 + 16 i

x^{3} = 343

8 x^{3} - 27 = 0

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

What are the solutions to the equation x^4-13x^2+40=0 ?
The solutions to the equation x^4-13x^2+40=0 are x=2sqrt(2),x=-2sqrt(2),x=sqrt(5),x=-sqrt(5)
Find the zeros of x^4-13x^2+40=0
The zeros of x^4-13x^2+40=0 are x=2sqrt(2),x=-2sqrt(2),x=sqrt(5),x=-sqrt(5)