What are the solutions to the equation (1-λ)(-λ)(2-λ)+λ=0 ?

The solutions to the equation (1-λ)(-λ)(2-λ)+λ=0 are λ=0,λ=(3+sqrt(5))/2 ,λ=(3-sqrt(5))/2

Find the zeros of (1-λ)(-λ)(2-λ)+λ=0

The zeros of (1-λ)(-λ)(2-λ)+λ=0 are λ=0,λ=(3+sqrt(5))/2 ,λ=(3-sqrt(5))/2

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(1 - λ) (- λ) (2 - λ) + λ = 0

λ = 0, λ = \frac{3 + 5}{2}, λ = \frac{3 - 5}{2}

Decimal Notation

λ = 0, λ = 2.61803 \dots, λ = 0.38196 \dots

Solution steps

(1 - λ) (- λ) (2 - λ) + λ = 0

Factor

(1 - λ) (- λ) (2 - λ) + λ : - λ (λ^{2} - 3 λ + 1)

- λ (λ^{2} - 3 λ + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

λ = 0 or λ^{2} - 3 λ + 1 = 0

Solve

λ^{2} - 3 λ + 1 = 0 : λ = \frac{3 + 5}{2}, λ = \frac{3 - 5}{2}

The solutions are

λ = 0, λ = \frac{3 + 5}{2}, λ = \frac{3 - 5}{2}

4 x^{5} = 144 x^{3}

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

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

(2 x + 7) (x^{2} - 15) = 0

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

What are the solutions to the equation (1-λ)(-λ)(2-λ)+λ=0 ?
The solutions to the equation (1-λ)(-λ)(2-λ)+λ=0 are λ=0,λ=(3+sqrt(5))/2 ,λ=(3-sqrt(5))/2
Find the zeros of (1-λ)(-λ)(2-λ)+λ=0
The zeros of (1-λ)(-λ)(2-λ)+λ=0 are λ=0,λ=(3+sqrt(5))/2 ,λ=(3-sqrt(5))/2