What are the solutions to the equation 3x^2-4x+11=0 ?

The solutions to the equation 3x^2-4x+11=0 are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3

Find the zeros of 3x^2-4x+11=0

The zeros of 3x^2-4x+11=0 are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3

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3 x^{2} - 4 x + 11 = 0

x = \frac{2}{3} + i \frac{29}{3}, x = \frac{2}{3} - i \frac{29}{3}

Solution steps

3 x^{2} - 4 x + 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 3 \cdot 11}{2 \cdot 3}

Simplify

(- 4)^{2} - 4 \cdot 3 \cdot 11 : 229 i

x_{1, 2} = \frac{- ( - 4 ) \pm 2 29 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 29 i}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2 29 i}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2 29 i}{2 \cdot 3} : \frac{2}{3} + i \frac{29}{3}

x = \frac{- ( - 4 ) - 2 29 i}{2 \cdot 3} : \frac{2}{3} - i \frac{29}{3}

The solutions to the quadratic equation are:

x = \frac{2}{3} + i \frac{29}{3}, x = \frac{2}{3} - i \frac{29}{3}

10 x^{2} + 29 x - 21

m^{- 2} \cdot n^{3}

z^{2} + 3 z - 10 = 0

\frac{2 a + 3 c}{2 a + c} - \frac{2 b - 3 a}{3 a + b} - \frac{2 c ( 3 a + b )}{6 a ^{2} + 2 ab + 3 a c + b c}

\frac{3}{5} r + \frac{1}{5} r = - 15 + 11

What are the solutions to the equation 3x^2-4x+11=0 ?
The solutions to the equation 3x^2-4x+11=0 are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3
Find the zeros of 3x^2-4x+11=0
The zeros of 3x^2-4x+11=0 are x= 2/3+i(sqrt(29))/3 ,x= 2/3-i(sqrt(29))/3