What are the solutions to the equation 45z^3+18z^2-5z-2=0 ?

The solutions to the equation 45z^3+18z^2-5z-2=0 are z=-2/5 ,z=-1/3 ,z= 1/3

Find the zeros of 45z^3+18z^2-5z-2=0

The zeros of 45z^3+18z^2-5z-2=0 are z=-2/5 ,z=-1/3 ,z= 1/3

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45 z^{3} + 18 z^{2} - 5 z - 2 = 0

z = - \frac{2}{5}, z = - \frac{1}{3}, z = \frac{1}{3}

Decimal Notation

z = - 0.4, z = - 0.33333 \dots, z = 0.33333 \dots

Solution steps

45 z^{3} + 18 z^{2} - 5 z - 2 = 0

Factor

45 z^{3} + 18 z^{2} - 5 z - 2 : (5 z + 2) (3 z + 1) (3 z - 1)

(5 z + 2) (3 z + 1) (3 z - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 z + 2 = 0 or 3 z + 1 = 0 or 3 z - 1 = 0

Solve

5 z + 2 = 0 : z = - \frac{2}{5}

Solve

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

Solve

3 z - 1 = 0 : z = \frac{1}{3}

The solutions are

z = - \frac{2}{5}, z = - \frac{1}{3}, z = \frac{1}{3}

- x^{3} - 2 x^{2} - 4 x - 8 = 0

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

9 x^{6} + 6 x^{4} - 10000 = 0

(x^{2} - 5) (x - 2) = 0

12 x^{3} + 27 x^{2} - 30 x = 0

What are the solutions to the equation 45z^3+18z^2-5z-2=0 ?
The solutions to the equation 45z^3+18z^2-5z-2=0 are z=-2/5 ,z=-1/3 ,z= 1/3
Find the zeros of 45z^3+18z^2-5z-2=0
The zeros of 45z^3+18z^2-5z-2=0 are z=-2/5 ,z=-1/3 ,z= 1/3