How does the discriminant relate to the notion of smoothness of a curve or surface?

The expression under the radical in the quadratic formula is called the discriminant, i.e., D = b2 – 4ac · The nature of the roots of a quadratic equation can be ... Solve for a variable, factor, expand, evaluate fractions, linear equations, quadratic equations, inequalities, systems of equations, matrices. 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 ... Jun 4, 2020 ... I wish I could use b^2-4ac>0 to check whether the people are real or not. May 20, 2024 ... The given form results in „division by 0“ if c = 0. Method 1: By completing the square, you get the known quadratic formula x = (-b +- sqrt(D)) / (2a). The discriminant of a quadratic is the expression inside the radical of the quadratic formula. b2−4(ac) b 2 - 4 ( 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 ... 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 ... - b Vb2-4ac. - b = Vb2-4ac. = b2- (b2-4ac). 2a(− b = √b² - 4ac hooray to writers who report and share something right! Howard Brand. Suitland High School. -b 소. / b2 - 4ac. 2a . Step 2: Write your answer in the appropriate form: 1. If b2 - 4ac > 0, then there are two real roots r1 and r2 and the general ...