How is the discriminant related to the concept of conserved quantities or invariants in physical systems described by quadratic Lagrangians or Hamiltonians?

The answer is statement 1 only, which would be selection A. A graph that meets the criteria expressed above would be: -x^2 + x - 1. Sep 3, 2020 ... Explanation. In the quadratic formula, −b±√(b2−4ac) / 2a, the term b2−4ac is called the discriminant. The discriminant plays an important role ... Jun 3, 2016 ... Let λ± = −b±. √ b2−4ac. 2a be the roots of p (λ) and suppose for the moment that b2 − 4ac 6= 0. From Eq. (1.3) it follows that for any ... The discriminant, b2 - 4ac, offers valuable information about the "nature" of the roots of a quadratic equation where a, b and c are rational values. It quickly ... and adding a constant (b/2a)2 so as to make a perfect square: a2x2 + bx + ... If b2 - 4ac is negative this solution will involve complex numbers, which ... ... 2 + q, the graph of y = f(x) has a turning point at (−p, q). • For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. 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 ... 2 Solving second-order polynomial equations. The roots of the following equation ax2 + bx + c = 0. (1) can be determined as: x1,2 = -b 소. / b2 - 4ac. 2a. (2). 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 ... Feb 22, 2011 ... ... b2– 4ac < 0. We are now able to compute the coefficient of ... if n is sufficiently large, max (a, b) << c, c > 0 and b2– 4ac < 0 ...