If 2 + i is a root of equation x3 - 5 x2 + 9x - 5 = 0, then the other roots are

Question

If 2 + i is a root of equation x3 - 5 x2 + 9x - 5 = 0, then the other roots are (A) 1 and 2-i (B) -1 and 3+i (C) 0 and 1 (D) -1 and i-2

Tardigrade Admin · Accepted Answer

Since complex roots always occur in pairs So, 2 - i is also a root of given equation. Given equation is x3 - 5x2 + 9x- 5 = 0. x = 1 satisfies this equation. ∴ Other roots are (2 - i) and 1 .

Q. If $2 + i$ is a root of equation $x^{3} - 5 x^{2} + 9 x - 5 = 0$ , then the other roots are

$1$ and $2 - i$

$- 1$ and $3 + i$

$0$ and $1$

$- 1$ and $i - 2$

Since complex roots always occur in pairs
So, $2 - i$ is also a root of given equation.
Given equation is $x^{3} - 5 x^{2} + 9 x - 5 = 0$ .
$x = 1$ satisfies this equation.
$∴$ Other roots are $(2 - i)$ and $1$ .

Q. If 2+i is a root of equation x3−5x2+9x−5=0, then the other roots are

1 and 2−i

−1 and 3+i

0 and 1

−1 and i−2