How does the concept of the discriminant differ in finite fields compared to real or complex numbers?

2. Over #: ax² + bx + c = 0. → x= -b±√b²-4ac га. "two issues: division by za. - is √b²-4ac EZZ with. In 24/m²: If gcd (za,n) = 1, then division га. Main goal: a. 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. 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 ... b = 1/2 a. 29. + á . Now a quantity like (.A + C)2 = 4AC + (A - C)2 may be ...

Find similar items here:

what is b 2 4ac

• Can the discriminant be used to derive the standard form of a parabola equation?
• If the roots are rational, is the discriminant necessarily a perfect square?
• How is the discriminant related to the concept of height of a polynomial or an algebraic number?
• What are the key features to consider when sketching a parabola?
• How can Vieta's formulas be used to find the discriminant?
• What are regular singular points of a differential equation, and how might a discriminant-like term appear in their analysis?
• How can the discriminant be used to determine if the roots are complex conjugates?
• How does the sign of the discriminant of a conic section relate to its type (ellipse, parabola, hyperbola)?
• The fundamental theorem of algebra guarantees the existence of roots, but the discriminant tells us about their nature. Can you elaborate on this?
• What does a zero discriminant indicate about the roots?