Question

The solutions to \[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$s://tex.z-dn.net/?f=The%20solutions%20to%5C%5B2x%5E2%20-%2010x%20%2B%2013%20%3D%200%5C%5Dare%20%24a%2Bbi%24%20and%20%24a-bi%2C%24%20where%20%24a%24%20and%20%24b%24%20are%20positive.%20What%20is%20%24a%5Ccdot%20b%3F%24" id="TexFormula1" title="The solutions to\[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$" alt="The solutions to\[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$" align="absmiddle" class="latex-formula">

Answer 1

Answer:

5/8

Step-by-step explanation:

(10 +/- √100-104)/4

(10 +/- 2i)/4

5/4 +/- 1/2i

5/4 * 1/2 = 5/8