What are the solutions to the equation 2z^3+z^2+10z+5=0 ?

The solutions to the equation 2z^3+z^2+10z+5=0 are z=-1/2 ,z=sqrt(5)i,z=-sqrt(5)i

Find the zeros of 2z^3+z^2+10z+5=0

The zeros of 2z^3+z^2+10z+5=0 are z=-1/2 ,z=sqrt(5)i,z=-sqrt(5)i

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2 z^{3} + z^{2} + 10 z + 5 = 0

z = - \frac{1}{2}, z = 5 i, z = - 5 i

Solution steps

2 z^{3} + z^{2} + 10 z + 5 = 0

Factor

2 z^{3} + z^{2} + 10 z + 5 : (2 z + 1) (z^{2} + 5)

(2 z + 1) (z^{2} + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 z + 1 = 0 or z^{2} + 5 = 0

Solve

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

Solve

z^{2} + 5 = 0 : z = 5 i, z = - 5 i

The solutions are

z = - \frac{1}{2}, z = 5 i, z = - 5 i

z^{8} = - 1

- 8.7 = l^{5}

m^{3} + m^{2} - 2 m = 0

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

(y - 4)^{4} = 0

What are the solutions to the equation 2z^3+z^2+10z+5=0 ?
The solutions to the equation 2z^3+z^2+10z+5=0 are z=-1/2 ,z=sqrt(5)i,z=-sqrt(5)i
Find the zeros of 2z^3+z^2+10z+5=0
The zeros of 2z^3+z^2+10z+5=0 are z=-1/2 ,z=sqrt(5)i,z=-sqrt(5)i