Are there any unexpected or surprising appearances of the discriminant in seemingly unrelated areas of mathematics?

2 )2 - b2. 4 + c. Quadratic formula: the roots of ax2 + bx + c are -b 소. /b2 - 4ac. 2a . Exponent rules: ab · ac = ab+c ab ac = ab−c. (ab)c = abc a1/b = b/a. The solution depends on the value of b2 - 4ac. This term is called the "discriminant". There are three cases: If (b2 - 4ac) > 0.0, two real roots exist (i.e ... Then, the discriminant A = b2-4ac satisfies: △ < a². Proof. If the ... + b 2 − a) . In conclusion, we believe that Lemma 1 can be a nice starting. Page 1. E = mc. 2 x = -b 소. / b2 - 4ac. 2a e iπ. +1 = 0 e x. = с. ∑ k=0 x n. /n! ∫ tanx dx = -ln(cosx). If b2 – 4ac < 0, then the graph is an ellipse (if b = 0 and a = c, the graph is a circle). Let's investigate it! Open the Quadratic Equations applet: In the ... x b ? b2 4ac. 2a. , x b ?b2 4ac. 2a . Page 4. 4. Now, suppose b ¡ 0 but b2 " 4ac (meaning that b2 is far larger than 4ac). An example of a quadratic equation ... Which of the following statements are true of the discriminant? ... The discriminant is b 2 - 4ac in the quadratic formula. The discriminant is the radicand of ... where a, b and c are real coefficients. The general solution to such an equation is given by the following formula, called the quadratic formula;. If b2 -4ac ... The expression under the radical in the quadratic formula is called the discriminant, i.e., D = b2 – 4ac · The nature of the roots of a quadratic equation can be ... We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ...