What are the solutions to the equation r^2+1/4 r+2=0 ?

The solutions to the equation r^2+1/4 r+2=0 are r=-1/8+i(sqrt(127))/8 ,r=-1/8-i(sqrt(127))/8

Find the zeros of r^2+1/4 r+2=0

The zeros of r^2+1/4 r+2=0 are r=-1/8+i(sqrt(127))/8 ,r=-1/8-i(sqrt(127))/8

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r^{2} + \frac{1}{4} r + 2 = 0

r = - \frac{1}{8} + i \frac{127}{8}, r = - \frac{1}{8} - i \frac{127}{8}

Solution steps

r^{2} + \frac{1}{4} r + 2 = 0

Multiply both sides by

4

4 r^{2} + r + 8 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 4 \cdot 8}{2 \cdot 4}

Simplify

1^{2} - 4 \cdot 4 \cdot 8 : 127 i

r_{1, 2} = \frac{- 1 \pm 127 i}{2 \cdot 4}

Separate the solutions

r_{1} = \frac{- 1 + 127 i}{2 \cdot 4}, r_{2} = \frac{- 1 - 127 i}{2 \cdot 4}

r = \frac{- 1 + 127 i}{2 \cdot 4} : - \frac{1}{8} + i \frac{127}{8}

r = \frac{- 1 - 127 i}{2 \cdot 4} : - \frac{1}{8} - i \frac{127}{8}

The solutions to the quadratic equation are:

r = - \frac{1}{8} + i \frac{127}{8}, r = - \frac{1}{8} - i \frac{127}{8}

9 + \frac{n}{3} > 16

\frac{3}{4 3}

\frac{1}{2} x^{2} + 5 x = - 14

x^{2} + 5 x + 7 = 0

x^{8} - 29 x^{4} + 100

What are the solutions to the equation r^2+1/4 r+2=0 ?
The solutions to the equation r^2+1/4 r+2=0 are r=-1/8+i(sqrt(127))/8 ,r=-1/8-i(sqrt(127))/8
Find the zeros of r^2+1/4 r+2=0
The zeros of r^2+1/4 r+2=0 are r=-1/8+i(sqrt(127))/8 ,r=-1/8-i(sqrt(127))/8