What are the solutions to the equation 101x^{100}+51x^{50}+1=0 ?

The solutions to the equation 101x^{100}+51x^{50}+1=0 are No Solution for x\in\mathbb{R}

Find the zeros of 101x^{100}+51x^{50}+1=0

The zeros of 101x^{100}+51x^{50}+1=0 are No Solution for x\in\mathbb{R}

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101 x^{100} + 51 x^{50} + 1 = 0

No Solution for x \in R

Solution steps

101 x^{100} + 51 x^{50} + 1 = 0

Rewrite the equation with

u = x^{2}, u^{25} = x^{50}

and

u^{50} = x^{100}

101 u^{50} + 51 u^{25} + 1 = 0

Solve

Substitute back

u = x^{2},

solve for

x

Solve

No Solution for

x \in R

Solve

No Solution for

x \in R

The solution is

No Solution for x \in R

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

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

2 x^{4} = 50

1 = x^{4}

22 x = x^{3} - 9 x^{2}

What are the solutions to the equation 101x^{100}+51x^{50}+1=0 ?
The solutions to the equation 101x^{100}+51x^{50}+1=0 are No Solution for x\in\mathbb{R}
Find the zeros of 101x^{100}+51x^{50}+1=0
The zeros of 101x^{100}+51x^{50}+1=0 are No Solution for x\in\mathbb{R}