Question

write a quadratic equation in the form x^2 + bx + c = 0 that has the following rootsroots : -10 + 8i

Answer 1

Given:

`x^2+bx+c=0`

The equation has the roots:

`-10\pm8i`

Let's find the equation.

We have the factors:

`\begin{gathered} -10\pm8i \\ x=-10\pm8i \\ x+10=\pm8i \end{gathered}`

Square both sides:

`\begin{gathered} (x+10)^2=\pm8i^2 \\ \\ x^2+20x+100=-64 \end{gathered}`

Add 64 to both sides of the equation to Equate to zero:

`\begin{gathered} x^2-20x+100+64=-64+64 \\ \\ x^2+20x+164=0 \end{gathered}`

Therefore, the quadratic equation is:

`x^2+20x+164=0`

ANSWER:

`x^2+20x+164=0`