Find the Exact Solutions to the Quadratic Equation in the Complex

question 9

Multiple Choice

Find the exact solutions to the quadratic equation in the complex numbers.
- $$( 2 x - 1 ) ^ { 2 } + 3 = 0$$

• A) \(\frac { 1 \pm \sqrt { 3 } } { 2 }\)
• B) \(2 \pm 2 \mathrm { i } \sqrt { 3 }\)
• C) \(\frac { 1 \pm 3 i } { 2 }\)
• D) \(\frac { 1 \pm i \sqrt { 3 } } { 2 }\)

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Definitions:

Hepatic Portal System

A network of veins that carries blood from the gastrointestinal organs and spleen to the liver.

Abdominal Viscera

The internal organs within the abdominal cavity, including the stomach, liver, intestines, and others.

Capillaries

Small blood vessels that facilitate the exchange of water, oxygen, carbon dioxide, and many other nutrients and waste substances between blood and surrounding tissues.

Splenic Vein

A blood vessel that drains blood from the spleen, pancreatic veins, and the short gastric veins, and empties into the portal vein.