Question

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

• A. 1 and 2 - i
• B. -1 and 3 + i
• C. 0 and 1
• D. – 1 and i - 2

Answer 1

The correct option is A 1 and 2 - i

As the coefficients are real and one root is 2+i, therefore, another root is (conjugate of 2 + i). Let the third root be a then sum of the roots $=2+i+2-i+\alpha$
$\Rightarrow -(-5)=4+\alpha \Rightarrow \alpha =1$
So, the other two roots are 2 - iand 1