What are the solutions to the equation 6x^4+7x^3-15x^2+7x-1=0 ?

The solutions to the equation 6x^4+7x^3-15x^2+7x-1=0 are x= 1/2 ,x= 1/3 ,x=-1+sqrt(2),x=-1-sqrt(2)

Find the zeros of 6x^4+7x^3-15x^2+7x-1=0

The zeros of 6x^4+7x^3-15x^2+7x-1=0 are x= 1/2 ,x= 1/3 ,x=-1+sqrt(2),x=-1-sqrt(2)

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6 x^{4} + 7 x^{3} - 15 x^{2} + 7 x - 1 = 0

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

Decimal Notation

x = 0.5, x = 0.33333 \dots, x = 0.41421 \dots, x = - 2.41421 \dots

Solution steps

6 x^{4} + 7 x^{3} - 15 x^{2} + 7 x - 1 = 0

Factor

6 x^{4} + 7 x^{3} - 15 x^{2} + 7 x - 1 : (2 x - 1) (3 x - 1) (x^{2} + 2 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

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

Solve

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

The solutions are

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

- x^{3} + 6 x^{2} - x - 22 = 0

t^{3} = 27

2 π x^{2} (\frac{9 - x}{3}) - 30 = 0

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

25 x^{3} - x = 0

What are the solutions to the equation 6x^4+7x^3-15x^2+7x-1=0 ?
The solutions to the equation 6x^4+7x^3-15x^2+7x-1=0 are x= 1/2 ,x= 1/3 ,x=-1+sqrt(2),x=-1-sqrt(2)
Find the zeros of 6x^4+7x^3-15x^2+7x-1=0
The zeros of 6x^4+7x^3-15x^2+7x-1=0 are x= 1/2 ,x= 1/3 ,x=-1+sqrt(2),x=-1-sqrt(2)