What are the solutions to the equation 6x^4-5x^3-38x^2-5x+6=0 ?

The solutions to the equation 6x^4-5x^3-38x^2-5x+6=0 are x=-2,x=3,x= 1/3 ,x=-1/2

Find the zeros of 6x^4-5x^3-38x^2-5x+6=0

The zeros of 6x^4-5x^3-38x^2-5x+6=0 are x=-2,x=3,x= 1/3 ,x=-1/2

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6 x^{4} - 5 x^{3} - 38 x^{2} - 5 x + 6 = 0

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

Decimal Notation

x = - 2, x = 3, x = 0.33333 \dots, x = - 0.5

Solution steps

6 x^{4} - 5 x^{3} - 38 x^{2} - 5 x + 6 = 0

Factor

6 x^{4} - 5 x^{3} - 38 x^{2} - 5 x + 6 : (x + 2) (x - 3) (3 x - 1) (2 x + 1)

(x + 2) (x - 3) (3 x - 1) (2 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x - 3 = 0 or 3 x - 1 = 0 or 2 x + 1 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 3 = 0 : x = 3

Solve

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

Solve

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

The solutions are

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

6 x^{4} - x^{3} + 5 x^{2} - x - 1 = 0

y, x = y^{3} + 1

2 x^{4} - 3 x^{2} - 20 = 0

x^{8} - 8 = 0

x^{4} - 3 x^{2} = - 2

What are the solutions to the equation 6x^4-5x^3-38x^2-5x+6=0 ?
The solutions to the equation 6x^4-5x^3-38x^2-5x+6=0 are x=-2,x=3,x= 1/3 ,x=-1/2
Find the zeros of 6x^4-5x^3-38x^2-5x+6=0
The zeros of 6x^4-5x^3-38x^2-5x+6=0 are x=-2,x=3,x= 1/3 ,x=-1/2