What are the solutions to the equation 6x^2-11x^4-2=0 ?

The solutions to the equation 6x^2-11x^4-2=0 are

Find the zeros of 6x^2-11x^4-2=0

The zeros of 6x^2-11x^4-2=0 are

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6 x^{2} - 11 x^{4} - 2 = 0

x = \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i

Solution steps

6 x^{2} - 11 x^{4} - 2 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 11 x^{4} + 6 x^{2} - 2 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

- 11 u^{2} + 6 u - 2 = 0

Solve

- 11 u^{2} + 6 u - 2 = 0 : u = \frac{3}{11} - i \frac{13}{11}, u = \frac{3}{11} + i \frac{13}{11}

u = \frac{3}{11} - i \frac{13}{11}, u = \frac{3}{11} + i \frac{13}{11}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{3}{11} - i \frac{13}{11} : x = \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i

Solve

x^{2} = \frac{3}{11} + i \frac{13}{11} : x = \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i

The solutions are

x = \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i

10 x^{4} - 3 x^{2} + 1 = 0

x^{3} + 7 x^{2} - 4 x - 28 = 0

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

3 x^{3} + 15 x^{2} = 18 x

2 x^{3} + 2 x^{2} - 3 x - 1 = 0

What are the solutions to the equation 6x^2-11x^4-2=0 ?
The solutions to the equation 6x^2-11x^4-2=0 are
Find the zeros of 6x^2-11x^4-2=0
The zeros of 6x^2-11x^4-2=0 are