Are there any models in statistical mechanics where a discriminant-like term determines the location of a critical point?

... 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. s = (-b – [b2 – 4ac])/2a. 1. Add them: r + s = (-b + -b)/2a = -b/a. 2. Multiply them: rs = ([-b]2 – [b2 – 4ac])/4a2 = c/a. back. Because the value of b2 – 4ac is less than zero, this equation will not have real solutions. Our answer will be 2x2 – 4x + 5 = 0. If we inspect all of the other ... 2. Over #: ax² + bx + c = 0. → x= -b±√b²-4ac га. "two issues: division by za. - is √b²-4ac EZZ with. In 24/m²: If gcd (za,n) = 1, then division га. Main goal: a. The quadratic formula solves quadratic equations. Given an equation in standard form, ax²+bx+c=0, the formula is: x=(-b±√(b²-4ac) ... 2−4(1)(−9)2 ... 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. Reduced forms. Consider a form ax2 + bxy + cy2. , with a, c > 0, and b2. -. 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 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 ... d=b2-4ac No solutions found Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : d-(b^2-4*a ...