What are the solutions to the equation roots 2x^4+5x^3+9x^2+15x+9 ?

The solutions to the equation roots 2x^4+5x^3+9x^2+15x+9 are x=-1,x=-3/2 ,x=sqrt(3)i,x=-sqrt(3)i

Find the zeros of roots 2x^4+5x^3+9x^2+15x+9

The zeros of roots 2x^4+5x^3+9x^2+15x+9 are x=-1,x=-3/2 ,x=sqrt(3)i,x=-sqrt(3)i

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roots

2 x^{4} + 5 x^{3} + 9 x^{2} + 15 x + 9

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

Solution steps

2 x^{4} + 5 x^{3} + 9 x^{2} + 15 x + 9

The roots are the intercepts with the x-axis

(y = 0)

2 x^{4} + 5 x^{3} + 9 x^{2} + 15 x + 9 = 0

Factor

2 x^{4} + 5 x^{3} + 9 x^{2} + 15 x + 9 : (x + 1) (2 x + 3) (x^{2} + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

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

Solve

x^{2} + 3 = 0 : x = 3 i, x = - 3 i

The solutions are

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

x^{4} - 8 x + 1 = 0

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

2 x + 4 = x^{3}

x^{4} - 10 x^{2} + 9

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

What are the solutions to the equation roots 2x^4+5x^3+9x^2+15x+9 ?
The solutions to the equation roots 2x^4+5x^3+9x^2+15x+9 are x=-1,x=-3/2 ,x=sqrt(3)i,x=-sqrt(3)i
Find the zeros of roots 2x^4+5x^3+9x^2+15x+9
The zeros of roots 2x^4+5x^3+9x^2+15x+9 are x=-1,x=-3/2 ,x=sqrt(3)i,x=-sqrt(3)i