What are the solutions to the equation 4x^4-13x^2+3=0 ?

The solutions to the equation 4x^4-13x^2+3=0 are x=sqrt(3),x=-sqrt(3),x= 1/2 ,x=-1/2

Find the zeros of 4x^4-13x^2+3=0

The zeros of 4x^4-13x^2+3=0 are x=sqrt(3),x=-sqrt(3),x= 1/2 ,x=-1/2

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4 x^{4} - 13 x^{2} + 3 = 0

x = 3, x = - 3, x = \frac{1}{2}, x = - \frac{1}{2}

Decimal Notation

x = 1.73205 \dots, x = - 1.73205 \dots, x = 0.5, x = - 0.5

Solution steps

4 x^{4} - 13 x^{2} + 3 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 13 u + 3 = 0

Solve

4 u^{2} - 13 u + 3 = 0 : u = 3, u = \frac{1}{4}

u = 3, u = \frac{1}{4}

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = \frac{1}{4} : x = \frac{1}{2}, x = - \frac{1}{2}

The solutions are

x = 3, x = - 3, x = \frac{1}{2}, x = - \frac{1}{2}

a^{3} - a^{7} - 5 - 3 = 0

x^{17} = x

x, x^{4} + y^{2} + x^{2} y^{2} + 16 x^{2} - 10 x^{2} y = 0

x, x^{3} d^{2} - x^{2} d^{1} - 3 x y = x^{2}

x^{3} - 2 x^{2} = 75

What are the solutions to the equation 4x^4-13x^2+3=0 ?
The solutions to the equation 4x^4-13x^2+3=0 are x=sqrt(3),x=-sqrt(3),x= 1/2 ,x=-1/2
Find the zeros of 4x^4-13x^2+3=0
The zeros of 4x^4-13x^2+3=0 are x=sqrt(3),x=-sqrt(3),x= 1/2 ,x=-1/2