What are the solutions to the equation 21x^3+x^2-5x-1=0 ?

The solutions to the equation 21x^3+x^2-5x-1=0 are x=-1/3 ,x=(1+2sqrt(2))/7 ,x=(1-2sqrt(2))/7

Find the zeros of 21x^3+x^2-5x-1=0

The zeros of 21x^3+x^2-5x-1=0 are x=-1/3 ,x=(1+2sqrt(2))/7 ,x=(1-2sqrt(2))/7

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21 x^{3} + x^{2} - 5 x - 1 = 0

x = - \frac{1}{3}, x = \frac{1 + 2 2}{7}, x = \frac{1 - 2 2}{7}

Decimal Notation

x = - 0.33333 \dots, x = 0.54691 \dots, x = - 0.26120 \dots

Solution steps

21 x^{3} + x^{2} - 5 x - 1 = 0

Factor

21 x^{3} + x^{2} - 5 x - 1 : (3 x + 1) (7 x^{2} - 2 x - 1)

(3 x + 1) (7 x^{2} - 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x + 1 = 0 or 7 x^{2} - 2 x - 1 = 0

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

7 x^{2} - 2 x - 1 = 0 : x = \frac{1 + 2 2}{7}, x = \frac{1 - 2 2}{7}

The solutions are

x = - \frac{1}{3}, x = \frac{1 + 2 2}{7}, x = \frac{1 - 2 2}{7}

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

0 = x^{4} - 10 x^{2} + 9

- 3 + c^{3} = 73

\frac{( x ^{5} + 20 )}{( - 3 )} = 4

15 x^{3} - 119 x^{2} - 10 x + 16 = 0

What are the solutions to the equation 21x^3+x^2-5x-1=0 ?
The solutions to the equation 21x^3+x^2-5x-1=0 are x=-1/3 ,x=(1+2sqrt(2))/7 ,x=(1-2sqrt(2))/7
Find the zeros of 21x^3+x^2-5x-1=0
The zeros of 21x^3+x^2-5x-1=0 are x=-1/3 ,x=(1+2sqrt(2))/7 ,x=(1-2sqrt(2))/7