## 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 $a=\frac{1}{2}$, $b=1$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula:

- $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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$x=-1+\pm \sqrt{-1}$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 1/2x^2+x+1=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=\frac{1}{2}, b=1 and c=1. Then substitute the values of the coefficients of the equation in the quadratic formula:<ul><li>\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</li></ul>. Calculate the power \sqrt{-1} using complex numbers. As in the equation we have the sign \pm, this produces two identical equations that differ in the sign of the term i. We write and solve both equations, one taking the positive sign, and the other taking the negative sign.