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

The solutions to the equation 3+5z+z^2=0 are z=(-5+sqrt(13))/2 ,z=(-5-sqrt(13))/2

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

The zeros of 3+5z+z^2=0 are z=(-5+sqrt(13))/2 ,z=(-5-sqrt(13))/2

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

z = \frac{- 5 + 13}{2}, z = \frac{- 5 - 13}{2}

Decimal Notation

z = - 0.69722 \dots, z = - 4.30277 \dots

Solution steps

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

Write in the standard form

a x^{2} + b x + c = 0

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

Solve with the quadratic formula

z_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

5^{2} - 4 \cdot 1 \cdot 3 = 13

z_{1, 2} = \frac{- 5 \pm 13}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- 5 + 13}{2 \cdot 1}, z_{2} = \frac{- 5 - 13}{2 \cdot 1}

z = \frac{- 5 + 13}{2 \cdot 1} : \frac{- 5 + 13}{2}

z = \frac{- 5 - 13}{2 \cdot 1} : \frac{- 5 - 13}{2}

The solutions to the quadratic equation are:

z = \frac{- 5 + 13}{2}, z = \frac{- 5 - 13}{2}

6 x^{2} + x - 15 = 8

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

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

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

x, 3 x^{2} = 0

What are the solutions to the equation 3+5z+z^2=0 ?
The solutions to the equation 3+5z+z^2=0 are z=(-5+sqrt(13))/2 ,z=(-5-sqrt(13))/2
Find the zeros of 3+5z+z^2=0
The zeros of 3+5z+z^2=0 are z=(-5+sqrt(13))/2 ,z=(-5-sqrt(13))/2