What is the Dedekind zeta function, and how does it encode information about the number field?

Jun 4, 2014 ... 3 Answers 3 ... Δ=b2−4ac>0 means that the equation has two real solutions. Δ=b2−4ac<0 means that the equation has no real solutions, but two ... There will be at most two real solutions to any quadratic equation. The value of b2 − 4ac (known as the discriminant) tells us how many real solutions there are ... Sep 3, 2020 ... Explanation. In the quadratic formula, −b±√(b2−4ac) / 2a, the term b2−4ac is called the discriminant. The discriminant plays an important role ... 17 In the quadratic formula, b2 − 4ac is called the discriminant. The function f(x) has a discriminant value of 8, and g(x) has a discriminant value of. Because the value of b2 – 4ac is less than zero, this equation will not have real solutions. Our answer will be 2x2 – 4x + 5 = 0. If we inspect all of the other ... Jun 3, 2016 ... Let λ± = −b±. √ b2−4ac. 2a be the roots of p (λ) and suppose for the moment that b2 − 4ac 6= 0. From Eq. (1.3) it follows that for any ... Which of the following statements are true of the discriminant? ... The discriminant is b 2 - 4ac in the quadratic formula. The discriminant is the radicand of ... (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 ... 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 ... The solution depends on the value of b2 - 4ac. This term is called the "discriminant". There are three cases: If (b2 - 4ac) > 0.0, two real roots exist (i.e ...