What is the index of a vector field, and how can it be computed?

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 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. Apr 11, 2018 ... For any equation of the form [ ax2 + bx + c = 0 ] the values of x ( the roots of the equation ) will always be [ ( -b ± ✓( b2 - 4ac ) ) / 2a ] ... Jun 4, 2020 ... I wish I could use b^2-4ac>0 to check whether the people are real or not. 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. Jan 24, 2019 ... ... 2+bx+c=0 if and only if. x={-b± √{b2-4ac}}/{2a}. LaTeX Original \documentclass{article} \usepackage{amssymb, mathrsfs, enumitem} \usepackage ... ... 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 ... F(z/Va- -b/2a) satisfies. (2) G(z)G(z + 1) = G(z2 + z - d), where d = (b2 - 4ac)/4a. The set Sd of roots of the polynomial G (z) is a finite nonempty set of ... The discriminant is B^2-4AC. Notice this is the portion of the formula inside the square root. If the discriminant = 0, then the formula degrades to x = -B ... Detailed step by step solution for k=(4ac-b^2)/(4a)