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

The solutions to the equation 2x^3+x^2+12x+6=0 are x=-1/2 ,x=sqrt(6)i,x=-sqrt(6)i

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

The zeros of 2x^3+x^2+12x+6=0 are x=-1/2 ,x=sqrt(6)i,x=-sqrt(6)i

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

x = - \frac{1}{2}, x = 6 i, x = - 6 i

Solution steps

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

Factor

2 x^{3} + x^{2} + 12 x + 6 : (2 x + 1) (x^{2} + 6)

(2 x + 1) (x^{2} + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 1 = 0 or x^{2} + 6 = 0

Solve

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

Solve

x^{2} + 6 = 0 : x = 6 i, x = - 6 i

The solutions are

x = - \frac{1}{2}, x = 6 i, x = - 6 i

x^{3} - 2 x + 1 x = - 2, 1.5

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

(x + 2)^{4} - 81 = 0

(4 x^{2} + 11 x - 3) (3 x + c) = 0

4 x^{3} - 9 x^{2} + 2 x = 0

What are the solutions to the equation 2x^3+x^2+12x+6=0 ?
The solutions to the equation 2x^3+x^2+12x+6=0 are x=-1/2 ,x=sqrt(6)i,x=-sqrt(6)i
Find the zeros of 2x^3+x^2+12x+6=0
The zeros of 2x^3+x^2+12x+6=0 are x=-1/2 ,x=sqrt(6)i,x=-sqrt(6)i