Are the roots rational or irrational when the discriminant is a perfect square and positive?

1. Let ƒ(x,y) = ax2 + bxy + cy2 be an indefinite binary quadratic form, with real coefficients a, b, c, and discriminant d = b2 —4ac. The expression under the radical in the quadratic formula is called the discriminant, i.e., D = b2 – 4ac · The nature of the roots of a quadratic equation can be ... 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 ... 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 ... Solve for a variable, factor, expand, evaluate fractions, linear equations, quadratic equations, inequalities, systems of equations, matrices. 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. 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 ... We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ... ... b2 − 4ac > 0. If the discriminant is positive then the quadratic has two real ... 2 + b. • How many real solutions does x2 + bx + 1 = 0 have? Find the ... 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 ...