What is the condition number of a problem, and how might the discriminant of a polynomial relate to the sensitivity of its roots to perturbations in the coefficients?

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 ... ... 2 + bxy + cy 2 of discriminant b 2 - 4ac = - d we can associate an ideal of norm a. Then the quadratic form associated to d with respect to this basis is Q ... Detailed step by step solution for k=(4ac-b^2)/(4a) However, we know there must be another independent solution. It's not obvious what that might be, but let's make the educated guess y(t) = C2teλ1t. 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. ... 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 ... Proposition 3 d=a+b+c positive integers with b2 >4ac. (i) When a ≡ b ≡ c ... 2+(b−δ)t. 4. ⊕ Z b+δ−2δt+. 4. ⊂ C. 2 . 4/8. 4. CM number fields. Let K be a ... Which of the following statements are true of the discriminant? ... The discriminant is b 2 - 4ac in the quadratic formula. The discriminant is the radicand of ... ax2 + bx + c = 0. might have the arithmetic if statement. if (b * b - 4 * a * c) 10, 20, 30 . Then if the discriminant b2 - 4ac is negative, the program jumps ... 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 ...