What are the solutions to the equation 1-1.2z+0.85*z^2=0 ?

The solutions to the equation 1-1.2z+0.85*z^2=0 are z= 12/17+i 14/17 ,z= 12/17-i 14/17

Find the zeros of 1-1.2z+0.85*z^2=0

The zeros of 1-1.2z+0.85*z^2=0 are z= 12/17+i 14/17 ,z= 12/17-i 14/17

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1 - 1.2 z + 0.85 \cdot z^{2} = 0

z = \frac{12}{17} + i \frac{14}{17}, z = \frac{12}{17} - i \frac{14}{17}

Solution steps

1 - 1.2 z + 0.85 z^{2} = 0

Multiply both sides by

100

100 - 120 z + 85 z^{2} = 0

Write in the standard form

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

85 z^{2} - 120 z + 100 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 120 ) \pm ( - 120 ) ^{2} - 4 \cdot 85 \cdot 100}{2 \cdot 85}

Simplify

(- 120)^{2} - 4 \cdot 85 \cdot 100 : 140 i

z_{1, 2} = \frac{- ( - 120 ) \pm 140 i}{2 \cdot 85}

Separate the solutions

z_{1} = \frac{- ( - 120 ) + 140 i}{2 \cdot 85}, z_{2} = \frac{- ( - 120 ) - 140 i}{2 \cdot 85}

z = \frac{- ( - 120 ) + 140 i}{2 \cdot 85} : \frac{12}{17} + i \frac{14}{17}

z = \frac{- ( - 120 ) - 140 i}{2 \cdot 85} : \frac{12}{17} - i \frac{14}{17}

The solutions to the quadratic equation are:

z = \frac{12}{17} + i \frac{14}{17}, z = \frac{12}{17} - i \frac{14}{17}

15 + 2 x^{2} = 177

- 3 x^{2} - 4 = 0

0.000006 x^{2} - 0.02 x + 25 = 15

(2 x + 1) (x - 1) = - 16 x - 8

a^{2} + 64 = 100

What are the solutions to the equation 1-1.2z+0.85*z^2=0 ?
The solutions to the equation 1-1.2z+0.85*z^2=0 are z= 12/17+i 14/17 ,z= 12/17-i 14/17
Find the zeros of 1-1.2z+0.85*z^2=0
The zeros of 1-1.2z+0.85*z^2=0 are z= 12/17+i 14/17 ,z= 12/17-i 14/17