+0  
 
+1
54
1
avatar+378 

 

Find the solutions x of the equation 2ix^2 + x +3i = 0
 

waffles  Nov 8, 2017

Best Answer 

 #1
avatar+18715 
+2

Find the solutions x of the equation 2ix^2 + x +3i = 0

 

\(\begin{array}{|rcll|} \hline \mathbf{ax^2+bx+c} &\mathbf{=}& \mathbf{0} \\ \mathbf{x} &\mathbf{=}& \mathbf{{-b \pm \sqrt{b^2-4ac} \over 2a}} \\\\ 2ix^2 + x +3i &=& 0 \quad & | \quad a = 2i \quad b = 1 \quad c = 3i \\ x &=& \dfrac{-1\pm \sqrt{1^2-4\cdot(2i) \cdot (3i)} } {2\cdot 2i } \\ &=& \dfrac{-1\pm \sqrt{1-24i^2} } {4i } \quad & | \quad i^2 = -1 \\ &=& \dfrac{-1\pm \sqrt{1+24} } {4i } \\ &=& \dfrac{-1\pm \sqrt{25} } {4i } \\ &=& \dfrac{-1\pm 5 } {4i } \cdot \dfrac{i}{i} \\ &=& \dfrac{ (-1\pm 5)i } {4i^2 } \quad & | \quad i^2 = -1 \\ &=& \dfrac{ (-1\pm 5)i } {-4} \\ \\ x_1 &=& \dfrac{ (-1+ 5)i } {-4} \\ &=& \dfrac{ 4i } {-4} \\ \mathbf{x_1} &\mathbf{=}& \mathbf{-i} \\\\ x_2 &=& \dfrac{ (-1- 5)i } {-4} \\ &=& \dfrac{ -6i } {-4} \\ \mathbf{x_2} &\mathbf{=}& \mathbf{ \dfrac{3} {2}i } \\ \hline \end{array}\)

 

laugh

heureka  Nov 8, 2017
Sort: 

1+0 Answers

 #1
avatar+18715 
+2
Best Answer

Find the solutions x of the equation 2ix^2 + x +3i = 0

 

\(\begin{array}{|rcll|} \hline \mathbf{ax^2+bx+c} &\mathbf{=}& \mathbf{0} \\ \mathbf{x} &\mathbf{=}& \mathbf{{-b \pm \sqrt{b^2-4ac} \over 2a}} \\\\ 2ix^2 + x +3i &=& 0 \quad & | \quad a = 2i \quad b = 1 \quad c = 3i \\ x &=& \dfrac{-1\pm \sqrt{1^2-4\cdot(2i) \cdot (3i)} } {2\cdot 2i } \\ &=& \dfrac{-1\pm \sqrt{1-24i^2} } {4i } \quad & | \quad i^2 = -1 \\ &=& \dfrac{-1\pm \sqrt{1+24} } {4i } \\ &=& \dfrac{-1\pm \sqrt{25} } {4i } \\ &=& \dfrac{-1\pm 5 } {4i } \cdot \dfrac{i}{i} \\ &=& \dfrac{ (-1\pm 5)i } {4i^2 } \quad & | \quad i^2 = -1 \\ &=& \dfrac{ (-1\pm 5)i } {-4} \\ \\ x_1 &=& \dfrac{ (-1+ 5)i } {-4} \\ &=& \dfrac{ 4i } {-4} \\ \mathbf{x_1} &\mathbf{=}& \mathbf{-i} \\\\ x_2 &=& \dfrac{ (-1- 5)i } {-4} \\ &=& \dfrac{ -6i } {-4} \\ \mathbf{x_2} &\mathbf{=}& \mathbf{ \dfrac{3} {2}i } \\ \hline \end{array}\)

 

laugh

heureka  Nov 8, 2017

9 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details