Question

2x^2 + 3ix + 2 = 0 solve quadratic equation ​

Answer 1

Answer:

$\large\boxed{X=\frac{1}{2}i, X=-2i }$

Step-by-step explanation:

To solve with quadratic equation, first you have to subsititute the x on both sides of the equation. Therefore, you can also solve with distributive property, complex arithmetic, standard complex form, and etc.

Given:

2x²+3ix+2=0

Solutions:

First, solve.

$\displaystyle x=a+bi$

$\displaystyle 2(a+bi)^2+3i(a+bi)+2=0$

Expand the form by using distributive property.

$\large\boxed{\textnormal{Distributive Property}}$

$\displaystyle a(b+c)=ab+ac$

$\displaystyle 2(a+bi)^2+3i(a+bi)+2=(2a^2-2b^2-3b+2)+i(3a+4ab)$

Make sure add equal sign to zero.

$\displaystyle (2a^2-2b^2-3b+2)+i(3a+4ab)=0$

Next, thing you do is rewrite the 0 of standard complex form.

$\large\boxed{\textnormal{Standard Complex Form}}$

$\displaystyle 0+0i$

$(2a^2-2b^2-3b+2)+i(3a+4ab)=0+0i$

Using a complex numbers it can be equal only if its real and imaginary parts are equal.

Rewrite the systems problem of expressions.

$\begin{bmatrix}2a^2-2b^2-3b+2=0\\3a+4ab=0\end{bmatrix}$

$\begin{bmatrix}2a^2-2b^2-3b+2=0\\3a+4ab=0\end{bmatrix}=\begin{pmatrix}b=\frac{1}{2},\:&a=0\\ b=-2,\:&a=0\end{pmatrix}$

Solve.

$\displaystyle x=a+bi$

$\large\boxed{X=\frac{1}{2},X=-2i}$

The quadratic equation of 2x²+3ix+2=0 is x=1/2i and x=-2i, which is our answer.