Can the discriminant be generalized to polynomials over finite fields?

If b2−4ac > 0 the equation has two distinct real number roots. Example. Study some of these examples: Find the roots of x2 + If b2 − 4ac < 0, we say the equation is elliptic. Example 1. • The wave equation utt − uxx = 0 is hyperbolic. • The Laplace equation. Page 1. E = mc. 2 x = -b 소. / b2 - 4ac. 2a e iπ. +1 = 0 e x. = с. ∑ k=0 x n. /n! ∫ tanx dx = -ln(cosx). Detailed step by step solution for k=(4ac-b^2)/(4a) 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 ... The quadratic formula, x=- b±sqrt(b^2-4ac)/2a, can be derived by completing the square on the general standard form a quadratic equation. 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. Then, the discriminant A = b2-4ac satisfies: △ < a². Proof. If the ... + b 2 − a) . In conclusion, we believe that Lemma 1 can be a nice starting. Summary. The symbol over the b2-4ac is called a 'radical', or a square root symbol; ' ± ' means 'plus or minus'; The DISCRIMINANT is the expression under ... and adding a constant (b/2a)2 so as to make a perfect square: a2x2 + bx + ... If b2 - 4ac is negative this solution will involve complex numbers, which ...