The discriminant of a polynomial is zero if and only if the polynomial has a multiple root (over an algebraically closed field). Can you explain why?

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. 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 ... Sep 12, 2024 ... 2. b2 - 4ac > 0. There are two distinct complex roots α 소 iβ. The general solution is y(x) = α1eα+iβx + α2eα−iβx which can be written as ... 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− ... Reduced forms. Consider a form ax2 + bxy + cy2. , with a, c > 0, and b2. -. b = 1/2 a. 29. + á 0 the equation has two distinct real number roots. Example. Study some of these examples: Find the roots of x2 +

Find similar items here:

what is b 2 4ac

• What is the genus of a curve, and how does it relate to its topology?
• Can the discriminant be a fraction?
• What type of roots are obtained when the discriminant is positive?
• Can the discriminant be used to analyze the behavior of solutions near caustics in optics or wave propagation?
• How can we construct a quadratic equation with a specific discriminant?
• Can the discriminant be generalized to polynomials over finite fields?
• How does the value of b² - 4ac change as the coefficients a, b, and c vary?
• How is the discriminant related to the theory of transcendence?
• How is the discriminant related to the genus of an algebraic curve?
• How is the discriminant used in the quadratic formula?