What are the solutions to the equation t^4-4t^2+3=0 ?

The solutions to the equation t^4-4t^2+3=0 are t=sqrt(3),t=-sqrt(3),t=1,t=-1

Find the zeros of t^4-4t^2+3=0

The zeros of t^4-4t^2+3=0 are t=sqrt(3),t=-sqrt(3),t=1,t=-1

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t^{4} - 4 t^{2} + 3 = 0

t = 3, t = - 3, t = 1, t = - 1

Decimal Notation

t = 1.73205 \dots, t = - 1.73205 \dots, t = 1, t = - 1

Solution steps

t^{4} - 4 t^{2} + 3 = 0

Rewrite the equation with

u = t^{2}

and

u^{2} = t^{4}

u^{2} - 4 u + 3 = 0

Solve

u^{2} - 4 u + 3 = 0 : u = 3, u = 1

u = 3, u = 1

Substitute back

u = t^{2},

solve for

t

Solve

t^{2} = 3 : t = 3, t = - 3

Solve

t^{2} = 1 : t = 1, t = - 1

The solutions are

t = 3, t = - 3, t = 1, t = - 1

x^{3} - x^{2} - 4 x - 6 = 0

25 x^{4} = 74 x^{2} - 49

x^{4} - 3 x^{3} + 6 x^{2} - 12 x + 8 = 0

x^{5} - 2 x^{4} - 24 x^{3} = 0

x^{3} - 2 x - 2 = 1.5

What are the solutions to the equation t^4-4t^2+3=0 ?
The solutions to the equation t^4-4t^2+3=0 are t=sqrt(3),t=-sqrt(3),t=1,t=-1
Find the zeros of t^4-4t^2+3=0
The zeros of t^4-4t^2+3=0 are t=sqrt(3),t=-sqrt(3),t=1,t=-1