Could the properties of discriminants be used in the design of signals or codes with specific properties?

The quadratic formula, x=- b±sqrt(b^2-4ac)/2a, can be derived by completing the square on the general standard form a quadratic equation. The discriminant of a quadratic is the expression inside the radical of the quadratic formula. b2−4(ac) b 2 - 4 ( a ... ... 2 (x + (b / 2a))2 = -4ac / 4a2 + b2 / 4a2 x + (b / 2a)2 = (b2 - 4ac) / 4a2 x + (b / 2a) = +/- sqrt ((b2 - 4ac) / 4a2) x = -b / 2a +/- sqrt(b2 - 4ac) / 2a Aug 30, 2011 ... As a→0, √b2−4ac→|b|. If b>0, only the minus sign in the denominator makes sense, giving you 2c−2b=−cb. If b<0, only the plus sign in the ... Hence, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression (b2 – 4ac) under the square root sign. We say this ... - b Vb2-4ac. - b = Vb2-4ac. = b2- (b2-4ac). 2a(− b = √b² - 4ac hooray to writers who report and share something right! Howard Brand. Suitland High School. The discriminant is 0, so the root is rational and the equation can be solved by factoring. In. , substitute: Since. , the equation has 2 real roots. b2 4ac>0. 17 In the quadratic formula, b2 − 4ac is called the discriminant. The function f(x) has a discriminant value of 8, and g(x) has a discriminant value of. Reduced forms. Consider a form ax2 + bxy + cy2. , with a, c > 0, and b2. -. Summary. The symbol over the b2-4ac is called a 'radical', or a square root symbol; ' ± ' means 'plus or minus'; The DISCRIMINANT is the expression under ...