Question

Find the quadratic equation with the roots indicated.{5 +/- i square root of 2}

Answer 1

Given:

`5\pm i√(2)`

The roots of the quadratic equation are;

`\begin{gathered} x=5\pm i√(2) \\ x=5+i√(2)\text{ OR }x=5-i√(2) \\ \\ The\text{ factors from the root are:} \\ (x-5-i√(2))=0\text{ OR }(x-5+i√(2))=0 \\ \\ As\text{ a quadratic equation:} \\ (x-5-i√(2))(x-5+i√(2))=0 \end{gathered}`

Expanding the factors further;

`\begin{gathered} (x-5-i√(2))(x-5+i√(2))=0 \\ x^2-5x+ix√(2)-5x+25-5i√(2)-ix√(2)+5i√(2)+2=0 \\ Collecting\text{ the like terms and simplifying further:} \\ x^2-5x-5x+ix√(2)-ix√(2)-5i√(2)+5i√(2)+25+2=0 \\ x^2-10x+27=0 \end{gathered}`

Therefore, the quadratic equation is;

`x^2-10x+27=0`