Can the discriminant be used to analyze the behavior of solutions of differential equations near singular points?

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 ... ) Suppose that a ~ 0 and that b2 — 4ac ≥ 0. Write the following number as an integer in standard form: ,_b_i/b2 —4ac\2. +b~. )+c. 2a. 2a. 0. Page 5. 6z4 —. 9z3 ... The discriminant is 0, so the root is rational and the equation can be solved by factoring. In. , substitute: Since. , the equation has 2 real roots. b2 4ac>0. ... b2 − 4ac > 0. If the discriminant is positive then the quadratic has two real ... 2 + b. • How many real solutions does x2 + bx + 1 = 0 have? Find the ... The discriminant (B2-4AC) is used to determine which conic section will result. If the discriminant is less than zero we have a circle (if A = C) or an ellipse; Square root in the denominator ; − b {\displaystyle -b}. {\displaystyle -b} ; + b 2 − 4 a c {\displaystyle \textstyle +{\sqrt {b^{2}-4ac}}}. {\displaystyle \ ... Detailed step by step solution for k=(4ac-b^2)/(4a) The discriminant, b2 - 4ac, offers valuable information about the "nature" of the roots of a quadratic equation where a, b and c are rational values. It quickly ... 2 Solving second-order polynomial equations. The roots of the following equation ax2 + bx + c = 0. (1) can be determined as: x1,2 = -b 소. / b2 - 4ac. 2a. (2). Jun 12, 2017 ... The question asks whether entire parabola is below x-axis. This will happen if discriminant is negative AND the parabola opens downward.