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Equation

Let z=5xi+x2-...

Question

Let $z = \frac{5 x i + (x^{2} - 5 x + 6) i^{2}}{i}, i^{2} = - 1$ is purely real number, then which of the following option(s) is/are correct?

x = 0

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x = 2

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x = 3

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x = 5

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Solution

The correct option is C $x = 3$
Given : $z = \frac{5 x i + (x^{2} - 5 x + 6) i^{2}}{i}$
$\Rightarrow z = 5 x + (x^{2} - 5 x + 6) i$
For purely real number
$I m (z) = 0 \Rightarrow x^{2} - 5 x + 6 = 0 \Rightarrow (x - 2) (x - 3) = 0 ∴ x = 2, 3$

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