What are the solutions to the equation x^4-19x^2+90=0 ?

The solutions to the equation x^4-19x^2+90=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3

Find the zeros of x^4-19x^2+90=0

The zeros of x^4-19x^2+90=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3

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x^{4} - 19 x^{2} + 90 = 0

x = 10, x = - 10, x = 3, x = - 3

Solution steps

x^{4} - 19 x^{2} + 90 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 19 u + 90 = 0

Solve

u^{2} - 19 u + 90 = 0 : u = 10, u = 9

u = 10, u = 9

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = 9 : x = 3, x = - 3

The solutions are

x = 10, x = - 10, x = 3, x = - 3

3 x^{1} - 5 x^{2} + 4 x^{3} = 7

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

8 x^{3} - 16 x^{2} - 16 x - 2 = 0

x^{5} - 81 x = 0

6 x^{3} - 21 x^{2} - 12 x = 0

What are the solutions to the equation x^4-19x^2+90=0 ?
The solutions to the equation x^4-19x^2+90=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3
Find the zeros of x^4-19x^2+90=0
The zeros of x^4-19x^2+90=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3