ExpandProcessLog\( \mathrm { 2 \cdot 3 \cdot \left(-4\right) = -24 } \)Str\( \mathrm { k^{2} - 24 = 0 } \)\( \mathrm { k^{2} + 2 \cdot 3 \cdot \left(-4\right) = 0 } \)\( \mathrm { k^{2} - 24 = 0 } \)SimplifyExpandProcessLogDetermine the discriminant of the quadratic equation to find the roots : \n \( \mathrm { a x ^ { 2 } + b x + c \Longrightarrow \Delta = b ^ { 2 } - 4 a c } \) \n \( \mathrm { a = 1 } \) \n \( \mathrm { b = 0 } \) \n \( \mathrm { c = -24 } \)Str\( \mathrm { \Delta = 0^{2} + \left(-4\right) \cdot \left(-24\right) } \)ProcessLogSimplify the exponents: \n \( \mathrm { 0^{2} = 0 } \)Str\( \mathrm { \Delta = \left(-4\right) \cdot \left(-24\right) } \)ProcessLog\( \mathrm { \left(-4\right) \cdot \left(-24\right) = 96 } \)Str\( \mathrm { \Delta = 96 } \)ProcessLogSince discriminant greater than zero the equation has two distinct real roots. Use the quadratic formula \( \mathrm { x _{ 1, 2 } = \displaystyle\frac { - b \pm \sqrt { \Delta } } { 2 a } } \) to determine roots.StrFirst root: \( \mathrm { k_{1} = \displaystyle\frac{0 + \sqrt{96}}{2} } \)ExpandProcessLogSimplify the root: \n \( \mathrm { \sqrt{96} = 4 \cdot \sqrt{6} } \)Str\( \mathrm { k_{1} = \displaystyle\frac{0 + 4 \cdot \sqrt{6}}{2} } \)ProcessLogSimplify the numerator and denominator: \n \( \mathrm { \displaystyle\frac{2 \cdot 2}{2} = 2 } \)Str\( \mathrm { k_{1} = 2 \cdot \sqrt{6} } \)\( \mathrm { k_{1} = \displaystyle\frac{0 + \sqrt{96}}{2} } \)\( \mathrm { k_{1} = 2 \cdot \sqrt{6} } \)SimplifyStrSecond root: \( \mathrm { k_{2} = \displaystyle\frac{0 - \sqrt{96}}{2} } \)ExpandProcessLogSimplify the root: \n \( \mathrm { \sqrt{96} = 4 \cdot \sqrt{6} } \)Str\( \mathrm { k_{2} = \displaystyle\frac{0 - 4 \cdot \sqrt{6}}{2} } \)ProcessLogSimplify the numerator and denominator: \n \( \mathrm { \displaystyle\frac{\left(-2\right) \cdot 2}{2} = -2 } \)Str\( \mathrm { k_{2} = - 2 \cdot \sqrt{6} } \)\( \mathrm { k_{2} = \displaystyle\frac{0 - \sqrt{96}}{2} } \)\( \mathrm { k_{2} = - 2 \cdot \sqrt{6} } \)Simplify\( \mathrm { k = \left\{- 2 \cdot \sqrt{6}, 2 \cdot \sqrt{6}\right\} } \)Determine the roots

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