https://artofproblemsolving.com/wiki/index.php?title=1965_AHSME_Problems/Problem_7&feed=atom&action=history 1965 AHSME Problems/Problem 7 - Revision history 2022-01-20T06:11:47Z Revision history for this page on the wiki MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=1965_AHSME_Problems/Problem_7&diff=84672&oldid=prev Crocodile 40: Created page with "Using Vieta's formulas, we can write the sum of the roots of any quadratic equation in the form $ax^2+bx+c = 0$ as $\frac{-b}{a}$, and the product as <ma..." 2017-03-12T17:23:06Z <p>Created page with &quot;Using Vieta&#039;s formulas, we can write the sum of the roots of any quadratic equation in the form &lt;math&gt;ax^2+bx+c = 0&lt;/math&gt; as &lt;math&gt;\frac{-b}{a}&lt;/math&gt;, and the product as &lt;ma...&quot;</p> <p><b>New page</b></p><div>Using Vieta's formulas, we can write the sum of the roots of any quadratic equation in the form &lt;math&gt;ax^2+bx+c = 0&lt;/math&gt; as &lt;math&gt;\frac{-b}{a}&lt;/math&gt;, and the product as &lt;math&gt;\frac{c}{a}&lt;/math&gt;.<br /> <br /> If &lt;math&gt;r&lt;/math&gt; and &lt;math&gt;s&lt;/math&gt; are the roots, then the sum of the reciprocals of the roots is &lt;math&gt;\frac{1}{r} + \frac{1}{s} = \frac{r+s}{rs}&lt;/math&gt;.<br /> <br /> Applying the formulas, we get &lt;math&gt;\frac{\frac{-b}{a}}{\frac{c}{a}}&lt;/math&gt;, or &lt;math&gt;\frac {-b}{c}&lt;/math&gt; =&gt; &lt;math&gt;\box{a}&lt;/math&gt;.</div> Crocodile 40