What are some applications of the discriminant in engineering and physics?

B2 – 4AC is the discriminant and identifies the type of conic. If B2 – 4AC < 0, then ellipse or circle; If B2 – 4AC = 0, then parabola ... where a, b and c are real coefficients. The general solution to such an equation is given by the following formula, called the quadratic formula;. If b2 -4ac ... (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 ... If B2 -4AC < 0, the conic is a circle, or an ellipse. If B2 - 4AC = 0, the conic is a parabola. Another way to classify conics has to do with ... If b2−4ac < 0, change format to linear combination of real-valued functions instead of complex valued func- tions by using Euler's formula. general solution is ... Sep 12, 2024 ... 2. b2 - 4ac > 0. There are two distinct complex roots α 소 iβ. The general solution is y(x) = α1eα+iβx + α2eα−iβx which can be written as ... 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 ... 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 ... 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 ... b± b. 2 4ac. 2a. E= dV dx. F=q E. V = 1. 4. Q r. R. 2 =N a. 2 x. 2 =2 Dt c=6 R. = v R.