How is the discriminant related to the concept of branching points in the theory of Riemann surfaces?

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. The solution depends on the value of b2 - 4ac. This term is called the "discriminant". There are three cases: If (b2 - 4ac) > 0.0, two real roots exist (i.e ... What is the probability that the equation Ax2 + Bx + C = 0 has two real roots? This is P(B2 - 4AC > 0). Note that since A,B,C ∈ [0, 1], if we ... Square root in the denominator ; − b {\displaystyle -b}. {\displaystyle -b} ; + b 2 − 4 a c {\displaystyle \textstyle +{\sqrt {b^{2}-4ac}}}. {\displaystyle \ ... Jun 3, 2016 ... Let λ± = −b±. √ b2−4ac. 2a be the roots of p (λ) and suppose for the moment that b2 − 4ac 6= 0. From Eq. (1.3) it follows that for any ... Detailed step by step solution for k=(4ac-b^2)/(4a) We consider the two solutions in (2) one at a time. With the plus, we get x+ = −b+ b2 − 4ac. 2a. = −b+ b2 − 4ac. 2a......... −b− b2 − 4ac. −b− ... Let gcd(a, b, c) = 1, D = b 2 - 4ac. Then as remarked in Mathews ([4, pages 132--133]), then there exist integers #, # such that a# 2 + b## + c# 2 = a ... Because the value of b2 – 4ac is less than zero, this equation will not have real solutions. Our answer will be 2x2 – 4x + 5 = 0. If we inspect all of the other ... ... byĵ + bzk̂ Magnitudes: |a⃗|=√{ax2 +ay2+az2} |b⃗|=√{bx2 +by2+bz2} Scalar ... 4ac}}/{2a} Work (W), Mechanical Energy (E, Kinetic Energy (K)) ...