What are the solutions to the equation 3x^3+x^2-13x+5=0 ?

The solutions to the equation 3x^3+x^2-13x+5=0 are x= 5/3 ,x=-1+sqrt(2),x=-1-sqrt(2)

Find the zeros of 3x^3+x^2-13x+5=0

The zeros of 3x^3+x^2-13x+5=0 are x= 5/3 ,x=-1+sqrt(2),x=-1-sqrt(2)

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3 x^{3} + x^{2} - 13 x + 5 = 0

x = \frac{5}{3}, x = - 1 + 2, x = - 1 - 2

Decimal Notation

x = 1.66666 \dots, x = 0.41421 \dots, x = - 2.41421 \dots

Solution steps

3 x^{3} + x^{2} - 13 x + 5 = 0

Factor

3 x^{3} + x^{2} - 13 x + 5 : (3 x - 5) (x^{2} + 2 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x - 5 = 0 : x = \frac{5}{3}

Solve

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

The solutions are

x = \frac{5}{3}, x = - 1 + 2, x = - 1 - 2

- x^{3} + 2 x = 0

8 x^{4} - 52 x^{3} + 84 x^{2} = 0

x^{4} + x^{2} + 25 = 0

z^{6} = i

x^{3} + 4 x^{2} = 38 x

What are the solutions to the equation 3x^3+x^2-13x+5=0 ?
The solutions to the equation 3x^3+x^2-13x+5=0 are x= 5/3 ,x=-1+sqrt(2),x=-1-sqrt(2)
Find the zeros of 3x^3+x^2-13x+5=0
The zeros of 3x^3+x^2-13x+5=0 are x= 5/3 ,x=-1+sqrt(2),x=-1-sqrt(2)