What are the solutions to the equation z^2-5z+84=0 ?

The solutions to the equation z^2-5z+84=0 are z= 5/2+i(sqrt(311))/2 ,z= 5/2-i(sqrt(311))/2

Find the zeros of z^2-5z+84=0

The zeros of z^2-5z+84=0 are z= 5/2+i(sqrt(311))/2 ,z= 5/2-i(sqrt(311))/2

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z^{2} - 5 z + 84 = 0

z = \frac{5}{2} + i \frac{311}{2}, z = \frac{5}{2} - i \frac{311}{2}

Solution steps

z^{2} - 5 z + 84 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot 84}{2 \cdot 1}

Simplify

(- 5)^{2} - 4 \cdot 1 \cdot 84 : 311 i

z_{1, 2} = \frac{- ( - 5 ) \pm 311 i}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 5 ) + 311 i}{2 \cdot 1}, z_{2} = \frac{- ( - 5 ) - 311 i}{2 \cdot 1}

z = \frac{- ( - 5 ) + 311 i}{2 \cdot 1} : \frac{5}{2} + i \frac{311}{2}

z = \frac{- ( - 5 ) - 311 i}{2 \cdot 1} : \frac{5}{2} - i \frac{311}{2}

The solutions to the quadratic equation are:

z = \frac{5}{2} + i \frac{311}{2}, z = \frac{5}{2} - i \frac{311}{2}

a^{2} + 9^{2} = 1 5^{2}

x^{2} - 13 x + 6 = 0

2 x^{2} + x - 20 = - 2 x^{2}

4 x^{2} - 40 x = 0

3 x^{2} + 11 x = 20

What are the solutions to the equation z^2-5z+84=0 ?
The solutions to the equation z^2-5z+84=0 are z= 5/2+i(sqrt(311))/2 ,z= 5/2-i(sqrt(311))/2
Find the zeros of z^2-5z+84=0
The zeros of z^2-5z+84=0 are z= 5/2+i(sqrt(311))/2 ,z= 5/2-i(sqrt(311))/2