How is the discriminant related to the Jacobian determinant in multivariable calculus?

Oct 20, 2011 ... (a) Prove that the discriminant D = b2 - 4ac ∈ K has a square root. /. D in L and that we have L = K(. /. D). [Hint: use the quadratic formula ... Detailed step by step solution for k=(4ac-b^2)/(4a) Jun 20, 2014 ... ... (b2-4ac ≥ 0) ⇒ (x = {-b-√{b2-4ac}}/{2a}) \lor (x = {-b+√{b2-4ac}}/{2a}). Please write complete proofs in each subquestion, without ... 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. 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; Mar 4, 2018 ... Explanation: · ⇒ · + · + · 1 · = · 0 · ← · in standard form. with a=2,b=3 and c=1. ⇒b2−4a ... Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. 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 ... May 20, 2024 ... The given form results in „division by 0“ if c = 0. Method 1: By completing the square, you get the known quadratic formula x = (-b +- sqrt(D)) / (2a). 2. Simple Gini Index with Quadratic Pen's Parade. Consider a quadratic ... b2 – 4ac < 0. We are now able to compute the coefficient of variation of ...