Are there other zeta functions associated with algebraic objects whose definition or properties involve discriminants?

Detailed step by step solution for k=(4ac-b^2)/(4a) Recall from precalcu- lus algebra that if the discriminant b2 - 4ac is positive, the equation (2) has two distinct ... 2 ) + b(c1y0. 1 + c2y0. 2) + c(c1y1 + ... 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 ... 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 ... Note: The number b2 - 4ac is called the discriminant of the equation ax2 + bx + c = 0. If the discriminant is negative then the equation has no real solutions. Feb 22, 2011 ... ... b2– 4ac < 0. We are now able to compute the coefficient of ... if n is sufficiently large, max (a, b) << c, c > 0 and b2– 4ac < 0 ... (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 ... 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 ... ... 2 + q, the graph of y = f(x) has a turning point at (−p, q). • For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. If b2 - 4ac is positive (>0) then we have 2 solutions. If b2 - 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/ ...