+0  
 
0
62
2
avatar

If the two roots of the quadratic 3x2+5x+k are -5+i sqrt(11)/6, -5-i sqrt(11)/6, what is k?

Guest Mar 16, 2018
Sort: 

2+0 Answers

 #1
avatar+9243 
+1

If the two roots of the quadratic 3x2+5x+k are -5+i sqrt(11)/6, -5-i sqrt(11)/6, what is k?

laugh

Omi67  Mar 16, 2018
 #2
avatar+19207 
+1

If the two roots of the quadratic 3x2+5x+k are ( -5+i sqrt(11))/6, ( -5-i sqrt(11) )/6, what is k?

 

\(\text{Let $ x_1 = \dfrac{ -5+i \sqrt{11} }{6} $ } \\ \text{Let $ x_2 = \dfrac{ -5-i \sqrt{11} }{6} $ } \)

 

\(\begin{array}{|rcll|} \hline 3x^2+5x+k &=& 0 \quad & | \quad : 3 \\ x^2+\dfrac{5}{3}x+\underbrace{\dfrac{k}{3}}_{=x_1x_2} &=& 0 \\\\ \dfrac{k}{3} &=& x_1x_2 \\\\ \dfrac{k}{3} &=& \left( \dfrac{ -5+i \sqrt{11} }{6} \right) \left( \dfrac{ -5-i \sqrt{11} }{6} \right) \\\\ \dfrac{k}{3} &=& \dfrac{ (-5)^2-(i \sqrt{11})^2 }{36} \\\\ \dfrac{k}{3} &=& \dfrac{25-i^2 \cdot 11 }{36} \quad & | \quad i^2 = -1 \\\\ \dfrac{k}{3} &=& \dfrac{25-(-1) \cdot 11 }{36} \\\\ \dfrac{k}{3} &=& \dfrac{25+11 }{36} \\\\ \dfrac{k}{3} &=& \dfrac{36 }{36} \\\\ \dfrac{k}{3} &=& 1 \\\\ \mathbf{k} & \mathbf{=} & \mathbf{3} \\ \hline \end{array}\)

 

 

laugh

heureka  Mar 16, 2018

33 Online Users

avatar
avatar
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