# Solve: ${x^2} - \left( {3\sqrt 2 + 2i} \right)x + 6i\sqrt 2 = 0$

Last updated date: 27th Mar 2023

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Answer

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310.5k+ views

Hint: - Factorize the quadratic equation

Given equation is

$

{x^2} - \left( {3\sqrt 2 + 2i} \right)x + 6i\sqrt 2 = 0 \\

\Rightarrow {x^2} - 3\sqrt 2 x - 2ix + 6i\sqrt 2 = 0 \\

\Rightarrow x\left( {x - 3\sqrt 2 } \right) - 2i\left( {x - 3\sqrt 2 } \right) = 0 \\

\Rightarrow \left( {x - 3\sqrt 2 } \right)\left( {x - 2i} \right) = 0 \\

\Rightarrow \left( {x - 3\sqrt 2 } \right) = 0,{\text{ }}\left( {x - 2i} \right) = 0 \\

\Rightarrow x = 3\sqrt 2 {\text{ and }}x = 2i \\

$

So, this is the required solution of the given equation.

Note: - In such types of questions the key concept is that we have to factorize the given equation, then we will get the required answer.

Given equation is

$

{x^2} - \left( {3\sqrt 2 + 2i} \right)x + 6i\sqrt 2 = 0 \\

\Rightarrow {x^2} - 3\sqrt 2 x - 2ix + 6i\sqrt 2 = 0 \\

\Rightarrow x\left( {x - 3\sqrt 2 } \right) - 2i\left( {x - 3\sqrt 2 } \right) = 0 \\

\Rightarrow \left( {x - 3\sqrt 2 } \right)\left( {x - 2i} \right) = 0 \\

\Rightarrow \left( {x - 3\sqrt 2 } \right) = 0,{\text{ }}\left( {x - 2i} \right) = 0 \\

\Rightarrow x = 3\sqrt 2 {\text{ and }}x = 2i \\

$

So, this is the required solution of the given equation.

Note: - In such types of questions the key concept is that we have to factorize the given equation, then we will get the required answer.

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