find a quadratic equation with the roots 14i and 14iSolution

find a quadratic equation with the roots -1+4i and -1-4i

Solution

Since the roots are given

we can find the factors as (x- (-1+4i) and (x- (-1-4i)).      //to find factors we write \"x - root\".

(x- (-1-4i)).      now we can open (x- (-1+4i) and (x- (-1-4i)).      //// if \"- sign\" is infront of a bracket then we open as -ve * -ve = +ve and -ve *+ve = -ve

so (x- (-1+4i) = (x+1 -4i)

and (x- (-1-4i)).= (x+1 +4i)     

now we just multiply these factors to find the quadratic equation.

(x+1 -4i) * (x+1 +4i) =0

(x^2 + x +4xi +x +1 +4i -4xi -4i +16) =0                    /// i*i = -1

we get

x^2 +2x +17=0

this is our quadratic equation.