Question

true or false10. If (1+i) is a root of a quadratic equation with real coefficients, the equation is y=x^2+2x+2

Answer 1

We know that a root of a quadratic function is a value of x that makes the function equal to 0.

So,

`\begin{gathered} \text{ if (1 + i) is a root of }y=x^2+2x+2 \\ \end{gathered}`

it must be fulfilled that,

`f(1+i)=0`

Now, we must replace (1 + i) in the function

`\begin{gathered} (1+i)^2+2(1+i)+2 \\ \\ \\ \end{gathered}`

solving the parentheses,

`=1+2i+i^2+2+2i+2`

Using that i^2 = -1

`=1+2i-1+2+2i+2`

grouping similar terms

`\begin{gathered} =(1-1+2+2)+(2i+2i) \\ \end{gathered}`

Finally, simplifying

`=4+4i`

We can see that

`4+4i\\e0`

So, (1 + i) is not a root of the equation.

The statement is false.