Can the discriminant be used to prove results in elementary number theory?

We can compute the discriminant of any power of a polynomial. For example, the quadratic discriminant is given by Δ 2 = b 2 − 4 a c \Delta_2 = b^2 - 4ac ... 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 ... Jan 21, 2020 ... Meoh789 Play Hard Win All The Best Online Games. Oct 24, 2008 ... (2) Let 4ac − b2 = 0. Using separation of variables, we obtain. Z dy ... b2 − 4ac − (2ad + b −. √ b2 − 4ac)et. √ b2−4ac . (2.7). To ... 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 ... Jun 4, 2014 ... 3 Answers 3 ... Δ=b2−4ac>0 means that the equation has two real solutions. Δ=b2−4ac<0 means that the equation has no real solutions, but two ... Jul 21, 2023 ... If a>0 and b^(2)-4ac=0, then the graph of y=ax^(2)+bx+c touches x -axis and lies above x -axis. Simplify. Check the solutions. Using the Discriminant, b2 − 4ac, to Determine the Number and Type of Solutions of a Quadratic Equation. 2. Simple Gini Index with Quadratic Pen's Parade. Consider a quadratic ... b2 – 4ac < 0. We are now able to compute the coefficient of variation of ... ... byĵ + bzk̂ Magnitudes: |a⃗|=√{ax2 +ay2+az2} |b⃗|=√{bx2 +by2+bz2} Scalar ... 4ac}}/{2a} Work (W), Mechanical Energy (E, Kinetic Energy (K)) ...