How is the discriminant related to the concept of curvature for curves in higher dimensions?

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 ... 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 ... ... b2 − 4ac > 0. If the discriminant is positive then the quadratic has two real ... 2 + b. • How many real solutions does x2 + bx + 1 = 0 have? Find the ... b = (2siso + ses) (Ved – Ves). c = ses (ses + siso) (Ves – Ved). Taking into account that smax > siso the answer of the sum is. x = {-b - √ (b2 – 4ac)} / 2a. Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. Let ax2 + bx + c = 0 be a quadratic equation with arbitrary coefficients a 6= 0, b and c. Its solution is given by the quadratic formula x1,2 = −b ±. √b2 − 4ac. 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. - b Vb2-4ac. - b = Vb2-4ac. = b2- (b2-4ac). 2a(− b = √b² - 4ac hooray to writers who report and share something right! Howard Brand. Suitland High School. 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 ... May 30, 2023 ... The square root of the discriminant gives us (Edit: double?) the distance that each quadratic root lies either side of where the axis of symmetry crosses the x ...