Question

Find a quadratic equation whose one root is (1-i)

Answer 1

one root is 1-i, Another root must be 1+i

Answer 2

Let the roots of the quadratic equation = α and β

Given:

α = 1 - i

We have, to find the quadratic equation = ?

Solution:

∴ β = 1 + i

We know that,

The sum of roots, α + β = 1 - i + 1 + i

= 2

The product of roots, αβ = (1 - i )(1 + i)

= $1^{2} -i^{2}$ = 2 [ ∵ $i^{2}$ = - 1]

∴ The quadratic equation is:

$x^2$ - (α + β)x + αβ = 0

⇒ $x^2$ - 2x + 2 = 0

Thus, the quadratic equation is "$x^2$ - 2x + 2 = 0".