What are the solutions to the equation 0=c^1(1/2)+c^2((sqrt(3))/2) ?

The solutions to the equation 0=c^1(1/2)+c^2((sqrt(3))/2) are c=0,c=-1/(sqrt(3))

Find the zeros of 0=c^1(1/2)+c^2((sqrt(3))/2)

The zeros of 0=c^1(1/2)+c^2((sqrt(3))/2) are c=0,c=-1/(sqrt(3))

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0 = c^{1} (\frac{1}{2}) + c^{2} (\frac{3}{2})

c = 0, c = - \frac{1}{3}

Decimal Notation

c = 0, c = - 0.57735 \dots

Solution steps

0 = c^{1} (\frac{1}{2}) + c^{2} (\frac{3}{2})

Expand

c^{1} (\frac{1}{2}) + c^{2} (\frac{3}{2}) : \frac{c}{2} + \frac{3 c ^{2}}{2}

0 = \frac{c}{2} + \frac{3 c ^{2}}{2}

Switch sides

\frac{c}{2} + \frac{3 c ^{2}}{2} = 0

Write in the standard form

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

\frac{3 c ^{2}}{2} + \frac{1 \cdot c}{2} = 0

Solve with the quadratic formula

c_{1, 2} = \frac{- \frac{1}{2} \pm ( \frac{1}{2} ) ^{2} - 4 \cdot \frac{3}{2} \cdot 0}{2 \cdot \frac{3}{2}}

(\frac{1}{2})^{2} - 4 \cdot \frac{3}{2} \cdot 0 = \frac{1}{2}

c_{1, 2} = \frac{- \frac{1}{2} \pm \frac{1}{2}}{2 \cdot \frac{3}{2}}

Separate the solutions

c_{1} = \frac{- \frac{1}{2} + \frac{1}{2}}{2 \cdot \frac{3}{2}}, c_{2} = \frac{- \frac{1}{2} - \frac{1}{2}}{2 \cdot \frac{3}{2}}

c = \frac{- \frac{1}{2} + \frac{1}{2}}{2 \frac{3}{2}} : 0

c = \frac{- \frac{1}{2} - \frac{1}{2}}{2 \frac{3}{2}} : - \frac{1}{3}

The solutions to the quadratic equation are:

c = 0, c = - \frac{1}{3}

- 6 y^{2} - 9 y + 1 = 0

8 x^{2} - 22 x + 5 = 0

x, x^{2} + 6 x - 3 = 0

3 x^{2} - 9 x + 4 = 0

4 y^{2} = 36

What are the solutions to the equation 0=c^1(1/2)+c^2((sqrt(3))/2) ?
The solutions to the equation 0=c^1(1/2)+c^2((sqrt(3))/2) are c=0,c=-1/(sqrt(3))
Find the zeros of 0=c^1(1/2)+c^2((sqrt(3))/2)
The zeros of 0=c^1(1/2)+c^2((sqrt(3))/2) are c=0,c=-1/(sqrt(3))