What are generalized curvatures, and how might a discriminant-like term appear?

Simplify. Check the solutions. Using the Discriminant, b2 − 4ac, to Determine the Number and Type of Solutions of a Quadratic Equation. (Algebra: solve quadratic equations) The two roots of a quadratic equation ax^2 + bx + c = 0 can be obtained using the following formula: b^2 - 4ac is ... (b) The point P = (1,−1,2) lies on both the paraboloid x2+y2 = z and the ... If a 6= 0 and b2 − 4ac > 0, then y has the form c1eαx + c2eβx where α ... The discriminant (B2-4AC) is used to determine which conic section will result. If the discriminant is less than zero we have a circle (if A = C) or an ellipse; 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 ... a x2 + bx +c = 0. has roots. x = {-b ± √{b2 - 4ac}}/{2a}. Newton's Method. If an initial guess x0 is close enough to a root of a function g, then the iteration ... Apr 2, 2012 ... ... b, and c. To calculate the roots of the equation the program calculates the discriminant D, given by D=b^2-4ac." Then it goes on to give me ... There will be at most two real solutions to any quadratic equation. The value of b2 − 4ac (known as the discriminant) tells us how many real solutions there are ... term with B + D. The result is. T. C2 — A2. B2. — D2. 1. V 2 H ~ 2 A H [ A C ( A + C)2. +. BD(B+D)2\. <2>. Now a quantity like (.A + C)2 = 4AC + (A - C)2 may be ... However, we know there must be another independent solution. It's not obvious what that might be, but let's make the educated guess y(t) = C2teλ1t.