Can the discriminant be used to analyze the sensitivity of the optimal solution to changes in the parameters?

Detailed step by step solution for k=(4ac-b^2)/(4a) 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 ... If b2 – 4ac < 0, then the graph is an ellipse (if b = 0 and a = c, the graph is a circle). Let's investigate it! Open the Quadratic Equations applet: In the ... ... 2 (x + (b / 2a))2 = -4ac / 4a2 + b2 / 4a2 x + (b / 2a)2 = (b2 - 4ac) / 4a2 x + (b / 2a) = +/- sqrt ((b2 - 4ac) / 4a2) x = -b / 2a +/- sqrt(b2 - 4ac) / 2a Oct 24, 2008 ... (2) Let 4ac − b2 = 0. Using separation of variables, we obtain. Z dy ... b2 − 4ac − (2ad + b −. √ b2 − 4ac)et. √ b2−4ac . (2.7). To ... Jul 21, 2023 ... If a>0 and b^(2)-4ac=0, then the graph of y=ax^(2)+bx+c touches x -axis and lies above x -axis. 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. b2 − 4ac = (−5)2 − 4 × 1 × 6=1 therefore, there are two solutions. Solution: Question 1 (continued). Substituting into the quadratic formula gives: x = −b ... 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 ... The solution depends on the value of b2 - 4ac. This term is called the "discriminant". There are three cases: If (b2 - 4ac) > 0.0, two real roots exist (i.e ...