How do these systems compute and utilize discriminants of polynomials?

Detailed step by step solution for k=(4ac-b^2)/(4a) Apr 2, 2012 ... ... b, and c. To calculate the roots of the equation the program calculates the discriminant D, given by D=b^2-4ac." Then it goes on to give me ... (Algebra: solve quadratic equations) The two roots of a quadratic equation ax^2 + bx + c = 0 can be obtained using the following formula: b^2 - 4ac is ... 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; Then, the discriminant A = b2-4ac satisfies: △ < a². Proof. If the ... + b 2 − a) . In conclusion, we believe that Lemma 1 can be a nice starting. 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. b = (2siso + ses) (Ved – Ves). c = ses (ses + siso) (Ves – Ved). Taking into account that smax > siso the answer of the sum is. x = {-b - √ (b2 – 4ac)} / 2a. 2 )2 - b2. 4 + c. Quadratic formula: the roots of ax2 + bx + c are -b 소. /b2 - 4ac. 2a . Exponent rules: ab · ac = ab+c ab ac = ab−c. (ab)c = abc a1/b = b/a. 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 ... If b2 - 4ac is positive (>0) then we have 2 solutions. If b2 - 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/ ...