What are the solutions to the equation 16q^4-8q^2+1=0 ?

The solutions to the equation 16q^4-8q^2+1=0 are q= 1/2 ,q=-1/2

Find the zeros of 16q^4-8q^2+1=0

The zeros of 16q^4-8q^2+1=0 are q= 1/2 ,q=-1/2

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16 q^{4} - 8 q^{2} + 1 = 0

q = \frac{1}{2}, q = - \frac{1}{2}

Decimal Notation

q = 0.5, q = - 0.5

Solution steps

16 q^{4} - 8 q^{2} + 1 = 0

Rewrite the equation with

u = q^{2}

and

u^{2} = q^{4}

16 u^{2} - 8 u + 1 = 0

Solve

16 u^{2} - 8 u + 1 = 0 : u = \frac{1}{4}

u = \frac{1}{4}

Substitute back

u = q^{2},

solve for

q

Solve

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

The solutions are

q = \frac{1}{2}, q = - \frac{1}{2}

x^{5} - 3 x^{4} - 2 x^{3} - x + 1 = 0

x^{4} - 20 x^{2} = - 64

8 x - 4 x^{3} = 0

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

x^{3} - 9 x - 7 = 0

What are the solutions to the equation 16q^4-8q^2+1=0 ?
The solutions to the equation 16q^4-8q^2+1=0 are q= 1/2 ,q=-1/2
Find the zeros of 16q^4-8q^2+1=0
The zeros of 16q^4-8q^2+1=0 are q= 1/2 ,q=-1/2