What are the solutions to the equation 6x^4+5x^3+25x^2+20x+4=0 ?

The solutions to the equation 6x^4+5x^3+25x^2+20x+4=0 are x=-1/2 ,x=-1/3 ,x=2i,x=-2i

Find the zeros of 6x^4+5x^3+25x^2+20x+4=0

The zeros of 6x^4+5x^3+25x^2+20x+4=0 are x=-1/2 ,x=-1/3 ,x=2i,x=-2i

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6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 = 0

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

Solution steps

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 = 0

Factor

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 : (2 x + 1) (3 x + 1) (x^{2} + 4)

(2 x + 1) (3 x + 1) (x^{2} + 4) = 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} + 4 = 0

Solve

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

Solve

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

Solve

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

The solutions are

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

x^{3} - 2 x^{2} + 62 - 0.5 = 0

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

x^{4} - x^{3} + 7 x^{2} - 9 x - 18 = 0

3 y^{3} - 11 y^{2} - 4 y = 0

n P^{5}

What are the solutions to the equation 6x^4+5x^3+25x^2+20x+4=0 ?
The solutions to the equation 6x^4+5x^3+25x^2+20x+4=0 are x=-1/2 ,x=-1/3 ,x=2i,x=-2i
Find the zeros of 6x^4+5x^3+25x^2+20x+4=0
The zeros of 6x^4+5x^3+25x^2+20x+4=0 are x=-1/2 ,x=-1/3 ,x=2i,x=-2i