What are the solutions to the equation k+k^3=68 ?

The solutions to the equation k+k^3=68 are k=4,k=-2+sqrt(13)i,k=-2-sqrt(13)i

Find the zeros of k+k^3=68

The zeros of k+k^3=68 are k=4,k=-2+sqrt(13)i,k=-2-sqrt(13)i

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k + k^{3} = 68

k = 4, k = - 2 + 13 i, k = - 2 - 13 i

Solution steps

k + k^{3} = 68

Move

68

to the left side

k + k^{3} - 68 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + k = 0

k^{3} + k - 68 = 0

Factor

k^{3} + k - 68 : (k - 4) (k^{2} + 4 k + 17)

(k - 4) (k^{2} + 4 k + 17) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

k - 4 = 0 or k^{2} + 4 k + 17 = 0

Solve

k - 4 = 0 : k = 4

Solve

k^{2} + 4 k + 17 = 0 : k = - 2 + 13 i, k = - 2 - 13 i

The solutions are

k = 4, k = - 2 + 13 i, k = - 2 - 13 i

z^{3} + 2 z^{2} + 21 z + 58 = 0

(x - 7)^{3} = 13

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

x, x^{3} + y^{2} = 1

(1 - y) (3 - y) (6 - y) = 18

What are the solutions to the equation k+k^3=68 ?
The solutions to the equation k+k^3=68 are k=4,k=-2+sqrt(13)i,k=-2-sqrt(13)i
Find the zeros of k+k^3=68
The zeros of k+k^3=68 are k=4,k=-2+sqrt(13)i,k=-2-sqrt(13)i