What are the solutions to the equation 6x^4+13x^3-8x^2-17x+6=0 ?

The solutions to the equation 6x^4+13x^3-8x^2-17x+6=0 are x=1,x=-2,x= 1/3 ,x=-3/2

Find the zeros of 6x^4+13x^3-8x^2-17x+6=0

The zeros of 6x^4+13x^3-8x^2-17x+6=0 are x=1,x=-2,x= 1/3 ,x=-3/2

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6 x^{4} + 13 x^{3} - 8 x^{2} - 17 x + 6 = 0

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

Decimal

x = 1, x = - 2, x = 0.33333 \dots, x = - 1.5

Solution steps

6 x^{4} + 13 x^{3} - 8 x^{2} - 17 x + 6 = 0

Factor

6 x^{4} + 13 x^{3} - 8 x^{2} - 17 x + 6 : (x - 1) (x + 2) (3 x - 1) (2 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x + 2 = 0 : x = - 2

Solve

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

Solve

2 x + 3 = 0 : x = - \frac{3}{2}

The solutions are

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

4 x^{4} + 2 x^{2} - 1 = 0

y, y^{2} = x^{2} - x^{4}

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

x^{3} + 5 x^{2} + 9 x + 5

x^{4} + 8 = - 9 x^{2}

What are the solutions to the equation 6x^4+13x^3-8x^2-17x+6=0 ?
The solutions to the equation 6x^4+13x^3-8x^2-17x+6=0 are x=1,x=-2,x= 1/3 ,x=-3/2
Find the zeros of 6x^4+13x^3-8x^2-17x+6=0
The zeros of 6x^4+13x^3-8x^2-17x+6=0 are x=1,x=-2,x= 1/3 ,x=-3/2