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4-2.Quadratic Equations and Inequations
hard
If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are
A
$1$ and $2 - i$
B
$-1$ and $3 + i$
C
$0$ and $1$
D
$-1$ and $i - 2$
Solution
(a) As the coefficients are real and one root is $2 + i,$ therefore, another root is $2 – i$ (conjugate of $2 + i$).
Let the third root be ? then sum of the roots $ = 2 + i + 2 – i + \alpha $
==> $ – ( – 5) = 4 + \alpha \Rightarrow \alpha = 1$
So, the other two roots are $2 – i$ and $1$.
Standard 11
Mathematics