Discriminant As we know, the discriminant of the polynomial f(x) = x2 + bx + c is D(f) = b2 4c, and only if f has a double root. What we weren’t taught when I was in school is that, if f, then the …

The discriminant of a polynomial c polynomial with oefficients in a fie d E. Let n = deg f(x) . Assume that n ≥ 2. Su n f(x) = Y (x − βi) i=1

Since R(f, g) is a symmetric function of the roots of f and g, it can be ex-pressed in terms of the coefficients. The expression is the following determinant. R(f, g) = ... ... ... of order m + n (with …

determine the exact multiplicity of a prime in the discriminant of K (we only know the multiplicity is positive for the rami ed primes).

Exercises 1 Discriminant In exercises 1{6 determine the discriminant of the given polynomial. * 1. x2 + bx + c * 2. x3 + 1 ** 3. x3 + x2 + x ** 4. x3 + x2 + 1 *** 5. x3 + ax2 + bx + c ** 6. x4 2 *** 7. …

Each graph below has 2 examples of quadratic curves with the allotted number of roots. The number of roots of a quadratic curve comes from the quadratic formula. The ± part gives us …

Chapter 5, Topic 5: Discriminant Discriminant: The expression that appears under the radical sign in the quadratic formula. Tells you about the "nature" of the roots: How many are there?