$$ \left. \begin{array} { l } { a = 2 \quad b = - 12 \quad c = 18 } \ { \lambda = \frac { - ( - 12 ) ^ { \pm } \sqrt { ( - 12 ) ^ { 2 } - 4 ( 2 ) ( 18 ) } } { 2 ( 2 ) } } \end{array} ight. $$

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$$ \left. \begin{array} { l } { a = 2 \quad b = - 12 \quad c = 18 } \ { \lambda = \frac { - ( - 12 ) ^ { \pm } \sqrt { ( - 12 ) ^ { 2 } - 4 ( 2 ) ( 18 ) } } { 2 ( 2 ) } } \end{array} ight. $$

UpStudy AI · Accepted Answer

The solution for $$ \lambda $$ is 0. To solve for the variable $$ \lambda $$ in the given equation, we need to first simplify the expression inside the square root and then solve for $$ \lambda $$. Let's go step by step. The given equation is: $$ \lambda = \frac{-(-12)^{\pm}\sqrt{(-12)^2 - 4(2)(18)}}{2(2)} $$ First, let's simplify the expression inside the square root: $$ (-12)^2 = 144 $$ $$ 4(2)(18) = 144 $$ So the expression inside the square root becomes: $$ \sqrt{144 - 144} = \sqrt{0} $$ Since the square root of 0 is 0, the expression simplifies to: $$ \lambda = \frac{-(-12)^{\pm} \cdot 0}{2(2)} $$ Now, since we have 0 in the numerator, the value of $$ \lambda $$ will be 0 regardless of the sign of $$ (-12)^{\pm} $$. Therefore, the final solution for $$ \lambda $$ is: $$ \lambda = 0 $$ This is the simplified and final answer for the given problem.

\( \left. \begin{array} { l } { a = 2 \quad b = - 12 \quad c = 18 } \\ { \lambda = \frac { - ( - 12 ) ^ { \pm } \sqrt { ( - 12 ) ^ { 2 } - 4 ( 2 ) ( 18 ) } } { 2 ( 2 ) } } \end{array} \right. \)

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\( \left. \begin{array} { l } { a = 2 \quad b = - 12 \quad c = 18 } \\ { \lambda = \frac { - ( - 12 ) ^ { \pm } \sqrt { ( - 12 ) ^ { 2 } - 4 ( 2 ) ( 18 ) } } { 2 ( 2 ) } } \end{array} \right. \)

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