If (1 + i) is a root of the equation x2 - x + (1 - i) = 0, then the other root is

Question

If (1 + i) is a root of the equation x2 - x + (1 - i) = 0, then the other root is (A) 1-i (B) i (C) -i (D) 2i

Tardigrade Admin · Accepted Answer

Equation, x2-x+(1-i)=0 and one root is given, say α=1+i and second root is β Since, the given root in complex form so, the other root is also complex form. Sum of the roots =α+β=-(-1) β=1-α=1-(1+i)=-i ∴ The other root is -i

Q. If $(1 + i)$ is a root of the equation $x^{2} - x + (1 - i) = 0$ , then the other root is

$1 - i$

$i$

$- i$

$2 i$

$- 2 i$

Equation, $x^{2} - x + (1 - i) = 0$
and one root is given, say $α = 1 + i$ and second root is $β$
Since, the given root in complex form so, the other root is also complex form.
Sum of the roots $= α + β = - (- 1)$
$β = 1 - α = 1 - (1 + i) = - i$
$∴$ The other root is $- i$

Q. If (1+i) is a root of the equation x2−x+(1−i)=0, then the other root is

1−i

i

−i

2i

−2i

Equation, x2−x+(1−i)=0 and one root is given, say α=1+i and second root is β Since, the given root in complex form so, the other root is also complex form. Sum of the roots =α+β=−(−1) β=1−α=1−(1+i)=−i ∴ The other root is −i