What are the solutions to the equation x^3-34x+12=0 ?

The solutions to the equation x^3-34x+12=0 are x=-6,x=3+sqrt(7),x=3-sqrt(7)

Find the zeros of x^3-34x+12=0

The zeros of x^3-34x+12=0 are x=-6,x=3+sqrt(7),x=3-sqrt(7)

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x^{3} - 34 x + 12 = 0

x = - 6, x = 3 + 7, x = 3 - 7

Decimal Notation

x = - 6, x = 5.64575 \dots, x = 0.35424 \dots

Solution steps

x^{3} - 34 x + 12 = 0

Factor

x^{3} - 34 x + 12 : (x + 6) (x^{2} - 6 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 6 = 0 : x = - 6

Solve

x^{2} - 6 x + 2 = 0 : x = 3 + 7, x = 3 - 7

The solutions are

x = - 6, x = 3 + 7, x = 3 - 7

r^{3} - 2 r^{2} - 5 r + 6 = 0

y, x = y^{3} + 5

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

x^{3} - 21 x - 20 = 0

y^{4} - 17 y^{2} + 16 = 0

What are the solutions to the equation x^3-34x+12=0 ?
The solutions to the equation x^3-34x+12=0 are x=-6,x=3+sqrt(7),x=3-sqrt(7)
Find the zeros of x^3-34x+12=0
The zeros of x^3-34x+12=0 are x=-6,x=3+sqrt(7),x=3-sqrt(7)