What are the solutions to the equation 6r^3-r^2-6r+1=0 ?

The solutions to the equation 6r^3-r^2-6r+1=0 are r= 1/6 ,r=-1,r=1

Find the zeros of 6r^3-r^2-6r+1=0

The zeros of 6r^3-r^2-6r+1=0 are r= 1/6 ,r=-1,r=1

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6 r^{3} - r^{2} - 6 r + 1 = 0

r = \frac{1}{6}, r = - 1, r = 1

Decimal Notation

r = 0.16666 \dots, r = - 1, r = 1

Solution steps

6 r^{3} - r^{2} - 6 r + 1 = 0

Factor

6 r^{3} - r^{2} - 6 r + 1 : (6 r - 1) (r + 1) (r - 1)

(6 r - 1) (r + 1) (r - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

6 r - 1 = 0 or r + 1 = 0 or r - 1 = 0

Solve

6 r - 1 = 0 : r = \frac{1}{6}

Solve

r + 1 = 0 : r = - 1

Solve

r - 1 = 0 : r = 1

The solutions are

r = \frac{1}{6}, r = - 1, r = 1

x = - 3 x^{4} + 2 x^{3} - 5 x + 8

x^{3} - 2 x^{2} + 1 = 0

(x + 1)^{3} = (2 x)^{3}

x, x^{3} + y^{3} = 8

2000 x^{3} = 1000

What are the solutions to the equation 6r^3-r^2-6r+1=0 ?
The solutions to the equation 6r^3-r^2-6r+1=0 are r= 1/6 ,r=-1,r=1
Find the zeros of 6r^3-r^2-6r+1=0
The zeros of 6r^3-r^2-6r+1=0 are r= 1/6 ,r=-1,r=1