Question

Describe the nature of the roots of this equation.2x^2-x+1=0O A. Two complex rootsO B. One real, double rootO C. Two real, rational rootsO D. Two real, irrational roots

Answer 1

A. Two complex roots

Step-by-step explanation

We want to describe the roots of the equation:

`2x^2\text{ - x + 1 = 0}`

Let us solve it with the quadratic formula.

For a quadratic equation:

`ax^2\text{ + bx + c = 0}`

The roots are gotten by using the formula:

`x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}`

So, we have that:

a = 2, b = -1, c = 1

So:

`\begin{gathered} x\text{ = }\frac{-(-1)\text{ }\pm\sqrt[]{(-1)^2\text{ - 4(2)(1)}}}{2\cdot2}=\frac{1\text{ }\pm\sqrt[]{1\text{ - 8}}}{4} \\ x\text{ = }\frac{1\text{ }\pm\sqrt[]{-7}}{4}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{7}\cdot\text{ }\sqrt[]{-1}}{4} \\ \Rightarrow\text{ x = }\frac{1\text{ + }\sqrt[]{7}i}{4}\text{ and }\frac{1\text{ - }\sqrt[]{7}i}{4} \end{gathered}`

As we can see, the two roots of the equation are complex.