First slide

Theory of equations

Question

If 1-2i is a root of the equation $z^{2} + α z + β = 0$ where $α, β \in R$ then the value of $α - β$ is

Moderate

A

12
B

10
C

-7
D

7

Solution

It is given that $a = 1 - 2 i is a root of z^{2} + α z + β = 0$
and imaginary roots of an equation with real coefficients occur in conjugate pairs. Therefore, the order root is $b = 1 + 2 i .$
$\Rightarrow a + b = 2 and a b = 5 \Rightarrow - α = 2 and β = 5 \Rightarrow α - β = - 7$

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