Solve the Equation in the Real Number System $2 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 0$

question 48

Multiple Choice

Solve the equation in the real number system.
- $2 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 0$

• A) \(\left\{ - \frac { \sqrt { 10 } } { 2 } , \frac { \sqrt { 10 } } { 2 } \right\}\)
• B) \(\{ 1 , - 2 \}\)
• C) \(\{ - 1,2 \}\)
• D) \(\left\{ - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right\}\)

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Definitions:

Real Solutions

The solutions of an equation that are real numbers, as opposed to imaginary or complex numbers.

Quadratic Equation

A mathematical equation where the highest power of an unknown variable is square.

Square Root Property

States that if x^2 = a, where a is a non-negative real number, then x = ±√a, identifying two possible solutions for x.

Factoring

The process of breaking down an expression into its simpler components or factors that, when multiplied together, result in the original expression.