What are orthogonal polynomials, and do discriminants of related polynomials have any significance?

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 ... Simplify. Check the solutions. Using the Discriminant, b2 − 4ac, to Determine the Number and Type of Solutions of a Quadratic Equation. F(z/Va- -b/2a) satisfies. (2) G(z)G(z + 1) = G(z2 + z - d), where d = (b2 - 4ac)/4a. The set Sd of roots of the polynomial G (z) is a finite nonempty set of ... We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ... 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 ... Detailed step by step solution for k=(4ac-b^2)/(4a) 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) 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 ... -b 소. / b2 - 4ac. 2a . Step 2: Write your answer in the appropriate form: 1. If b2 - 4ac > 0, then there are two real roots r1 and r2 and the general ... 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 ...