Can the discriminant be used to analyze the stability of fluid flows described by nonlinear partial differential equations?

The answer is statement 1 only, which would be selection A. A graph that meets the criteria expressed above would be: -x^2 + x - 1. Hence, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression (b2 – 4ac) under the square root sign. We say this ... 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. (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 ... Detailed step by step solution for k=(4ac-b^2)/(4a) 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 ... Feb 22, 2011 ... ... b2– 4ac < 0. We are now able to compute the coefficient of ... if n is sufficiently large, max (a, b) << c, c > 0 and b2– 4ac < 0 ... May 31, 2018 ... ... (2,Z) is denoted by h(d) and called the class number of binary quadratic forms of discriminant d. Note: d = b2 − 4ac, so d ≡ 0 or 1 mod 4. We consider the two solutions in (2) one at a time. With the plus, we get x+ = −b+ b2 − 4ac. 2a. = −b+ b2 − 4ac. 2a......... −b− b2 − 4ac. −b− ... 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 ...