Question

solve this quadratic equation. 3x^2+8ix+3=0​

Answer 1

Simplifying

3x2 + 8ix + 3 = 0

Reorder the terms:

3 + 8ix + 3x2 = 0

Solving

3 + 8ix + 3x2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + 8ix + -3 + 3x2 = 0 + -3

Reorder the terms:

3 + -3 + 8ix + 3x2 = 0 + -3

Combine like terms: 3 + -3 = 0

0 + 8ix + 3x2 = 0 + -3

8ix + 3x2 = 0 + -3

Combine like terms: 0 + -3 = -3

8ix + 3x2 = -3

Add '-3x2' to each side of the equation.

8ix + 3x2 + -3x2 = -3 + -3x2

Combine like terms: 3x2 + -3x2 = 0

8ix + 0 = -3 + -3x2

8ix = -3 + -3x2

Divide each side by '8x'.

i = -0.375x-1 + -0.375x

Simplifying

i = -0.375x-1 + -0.375x

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

${\boxed{\bigstar{{Equation\;is\;in\;the\;form\;of:-}}}}$

ax² + bx + c

Hence,

a = 3

b = 8i

c = 3

${\boxed{\bigstar{{Using\;Rule\;of\; Discriminant}}}}$

d = b² - 4ac

= [(8i)² - 4 × 3 × 3 × 3]

= (-64 - 36)

= -100

${\boxed{\bigstar{{Equation\;is\;complex}}}}$

$\tt{\rightarrow\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$

$\tt{\rightarrow\dfrac{-8i\pm \sqrt{(8i)^2-4\times 3\times 3}}{2\times 3}}$

$\tt{\rightarrow\dfrac{-8i\pm \sqrt{-100}}{6}}$

$\tt{\rightarrow\dfrac{-8i\pm 10i}{6}}$

Hence,

Roots are :-

$\tt{\rightarrow\dfrac{-8i+10i}{6}}$

$\tt{\rightarrow\dfrac{-8i-10i}{6}}$

Hence,

$\tt{\rightarrow Set=\dfrac{1}{3}i\;,\; -3 i}$