What are the solutions to the equation λ^2-2λ-1=0 ?

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

Find the zeros of λ^2-2λ-1=0

The zeros of λ^2-2λ-1=0 are λ=1+sqrt(2),λ=1-sqrt(2)

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λ^{2} - 2 λ - 1 = 0

λ = 1 + 2, λ = 1 - 2

Decimal Notation

λ = 2.41421 \dots, λ = - 0.41421 \dots

Solution steps

λ^{2} - 2 λ - 1 = 0

Solve with the quadratic formula

λ_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 1) = 22

λ_{1, 2} = \frac{- ( - 2 ) \pm 2 2}{2 \cdot 1}

Separate the solutions

λ_{1} = \frac{- ( - 2 ) + 2 2}{2 \cdot 1}, λ_{2} = \frac{- ( - 2 ) - 2 2}{2 \cdot 1}

λ = \frac{- ( - 2 ) + 2 2}{2 \cdot 1} : 1 + 2

λ = \frac{- ( - 2 ) - 2 2}{2 \cdot 1} : 1 - 2

The solutions to the quadratic equation are:

λ = 1 + 2, λ = 1 - 2

(x^{2} - 2 x + 4) = 0

15 x^{2} - 9 x - 6 = 0

(2 x + 3) (x - 6) = 0

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

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

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