What are the solutions to the equation roots x^2+xa+a^2 ?

The solutions to the equation roots x^2+xa+a^2 are x=-a/2+i(sqrt(3)a)/2 ,x=-a/2-i(sqrt(3)a)/2

Find the zeros of roots x^2+xa+a^2

The zeros of roots x^2+xa+a^2 are x=-a/2+i(sqrt(3)a)/2 ,x=-a/2-i(sqrt(3)a)/2

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roots

x^{2} + x a + a^{2}

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

Solution steps

x^{2} + x a + a^{2}

The roots are the intercepts with the x-axis

(y = 0)

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

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- a \pm a ^{2} - 4 \cdot 1 \cdot a ^{2}}{2 \cdot 1}

Simplify

a^{2} - 4 \cdot 1 \cdot a^{2} : 3 ia

x_{1, 2} = \frac{- a \pm 3 ia}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- a + 3 ia}{2 \cdot 1}, x_{2} = \frac{- a - 3 ia}{2 \cdot 1}

x = \frac{- a + 3 ia}{2 \cdot 1} : - \frac{a}{2} + i \frac{3 a}{2}

x = \frac{- a - 3 ia}{2 \cdot 1} : - \frac{a}{2} - i \frac{3 a}{2}

The solutions to the quadratic equation are:

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

- x^{2} - 0 x + 16 = 0

2 p^{2} + 2 p - 84 = 0

y, x^{2} y^{2} + x y = 12

3 y^{2} + 7 y - 10 = 0

30 + 13 x - 3 x^{2} = 0

What are the solutions to the equation roots x^2+xa+a^2 ?
The solutions to the equation roots x^2+xa+a^2 are x=-a/2+i(sqrt(3)a)/2 ,x=-a/2-i(sqrt(3)a)/2
Find the zeros of roots x^2+xa+a^2
The zeros of roots x^2+xa+a^2 are x=-a/2+i(sqrt(3)a)/2 ,x=-a/2-i(sqrt(3)a)/2