http://far.chickenkiller.com/tags/quadratic_function/ Recent content in Quadratic_function on far.chickenkiller.com fkz on riseup dot net (Farooq Karimi Zadeh) fkz on riseup dot net (Farooq Karimi Zadeh)Hugo -- gohugo.ioen-us(C) Some rights are reserved under CC-BY-SA 4.0 for Farooq Karimi Zadeh Mon, 17 Jan 2022 13:38:33 +0330http://far.chickenkiller.com/math/when-a-quadratic-equation-does-not-have-real-roots/Mon, 17 Jan 2022 13:38:33 +0330http://far.chickenkiller.com/math/when-a-quadratic-equation-does-not-have-real-roots/ <p>For any equation as $ax^2 + bx + c = 0$ we have $b^2 - 4ac$ or $\Delta$ smaller than zero thus having no real roots if:</p> <ol> <li>$a, c &gt; |b|$</li> <li>$a = b = c$</li> <li>$a = b$ and $c &gt; b$ for any positive $b$. You can swap $a$ and $c$.</li> </ol> <p>I have proved these but since it&rsquo;s trivial, I did not write them here.</p>