What are the solutions to the equation λ^3-21λ^2+84λ-64=0 ?

The solutions to the equation λ^3-21λ^2+84λ-64=0 are λ=1,λ=4,λ=16

Find the zeros of λ^3-21λ^2+84λ-64=0

The zeros of λ^3-21λ^2+84λ-64=0 are λ=1,λ=4,λ=16

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λ^{3} - 21 λ^{2} + 84 λ - 64 = 0

λ = 1, λ = 4, λ = 16

Solution steps

λ^{3} - 21 λ^{2} + 84 λ - 64 = 0

Factor

λ^{3} - 21 λ^{2} + 84 λ - 64 : (λ - 1) (λ - 4) (λ - 16)

(λ - 1) (λ - 4) (λ - 16) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

λ - 1 = 0 or λ - 4 = 0 or λ - 16 = 0

Solve

λ - 1 = 0 : λ = 1

Solve

λ - 4 = 0 : λ = 4

Solve

λ - 16 = 0 : λ = 16

The solutions are

λ = 1, λ = 4, λ = 16

- x^{3} + x^{2} - 25 x + 25 = 0

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

15 x^{4} - 8 x^{3} + 54 x^{2} + 18 x - 4 = 0

- x^{3} + 6 x^{2} = 0

x^{2} + x^{3} = 5

What are the solutions to the equation λ^3-21λ^2+84λ-64=0 ?
The solutions to the equation λ^3-21λ^2+84λ-64=0 are λ=1,λ=4,λ=16
Find the zeros of λ^3-21λ^2+84λ-64=0
The zeros of λ^3-21λ^2+84λ-64=0 are λ=1,λ=4,λ=16