Construct a quadratic equation with real co-efficients one of whose root is $(2 + 3 i)$ .

Open in App

Solution

As we are to find a quadratic equation with real co-efficient whose one root is $(2 + 3 i)$ then its other root is $(2 - 3 i)$ (conjugate of the given one).
So the quadratic equation is ,
$x^{2} - x {(2 + 3 i) + (2 - 3 i)} + (2 + 3 i) (2 - 3 i) = 0$
or, $x^{2} - 4 x + 13 = 0$ .

Suggest Corrections

Similar questions

3 - 2 i

\frac{1}{2} (1 + \sqrt{- 3})

3 - 2 i

\frac{\sqrt{2} + \sqrt{3} i}{\sqrt{2} - \sqrt{3} i}

\frac{\sqrt{2} - \sqrt{3} i}{\sqrt{2} + \sqrt{3} i}

i = \sqrt{- 1}

\frac{1}{2 + \sqrt{5}}

Join BYJU'S Learning Program