What are the solutions to the equation 6x+21x^2+12x^3=0 ?

The solutions to the equation 6x+21x^2+12x^3=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8

Find the zeros of 6x+21x^2+12x^3=0

The zeros of 6x+21x^2+12x^3=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8

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6 x + 21 x^{2} + 12 x^{3} = 0

x = 0, x = \frac{- 7 + 17}{8}, x = \frac{- 7 - 17}{8}

Decimal Notation

x = 0, x = - 0.35961 \dots, x = - 1.39038 \dots

Solution steps

6 x + 21 x^{2} + 12 x^{3} = 0

Factor

6 x + 21 x^{2} + 12 x^{3} : 3 x (4 x^{2} + 7 x + 2)

3 x (4 x^{2} + 7 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 x^{2} + 7 x + 2 = 0

Solve

4 x^{2} + 7 x + 2 = 0 : x = \frac{- 7 + 17}{8}, x = \frac{- 7 - 17}{8}

The solutions are

x = 0, x = \frac{- 7 + 17}{8}, x = \frac{- 7 - 17}{8}

2 x^{5} - 4 x - 7 = 0

2 x^{3} - x^{2} + 11 x - 5 = 0

12 (k (k^{2} - 4 k + 1) + 6) = 0

x^{3} - 5 x^{2} + 14 x = 0

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

What are the solutions to the equation 6x+21x^2+12x^3=0 ?
The solutions to the equation 6x+21x^2+12x^3=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8
Find the zeros of 6x+21x^2+12x^3=0
The zeros of 6x+21x^2+12x^3=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8