Final Answer
Step-by-step Solution
Problem to solve:
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To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-1$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula:
- $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
Calculate the power $\sqrt{-3}$ using complex numbers
Calculate the power $\sqrt{-3}$ using complex numbers
Expand the fraction $\frac{1+1.732051i}{2}$ into $2$ simpler fractions with common denominator $2$
Take $\frac{\sqrt{3}}{2}$ out of the fraction
Simplify
Expand the fraction $\frac{1-1.732051i}{2}$ into $2$ simpler fractions with common denominator $2$
Take $\frac{-\sqrt{3}}{2}$ out of the fraction
Simplify