What is the definition of the discriminant of an algebraic variety?

The discriminant of a quadratic is the expression inside the radical of the quadratic formula. b2−4(ac) b 2 - 4 ( a ... Apr 7, 2014 ... I know how to derive the quadratic formula but not the alternate. -b ± √(b^2 - 4ac) b ± √(b^2 - 4ac) ... x1=(-b+sqrt(b^2-4ac))/2a=(-b+sqrt ... Sep 3, 2020 ... Explanation. In the quadratic formula, −b±√(b2−4ac) / 2a, the term b2−4ac is called the discriminant. The discriminant plays an important role ... If b2−4ac > 0 the equation has two distinct real number roots. Example. Study some of these examples: Find the roots of x2 + 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 ... 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. The quadratic formula, x=- b±sqrt(b^2-4ac)/2a, can be derived by completing the square on the general standard form a quadratic equation. d=b2-4ac No solutions found Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : d-(b^2-4*a ... Recall from precalcu- lus algebra that if the discriminant b2 - 4ac is positive, the equation (2) has two distinct ... 2 ) + b(c1y0. 1 + c2y0. 2) + c(c1y1 + ... 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 ] ...