Are there any famous problems in mathematics whose solution involves the discriminant?

Feb 2, 2020 ... Overview of the discriminant from quadratic formula and its interpretation. Click here to see all quadratic formula videos: ... 2 Solving second-order polynomial equations. The roots of the following equation ax2 + bx + c = 0. (1) can be determined as: x1,2 = -b 소. / b2 - 4ac. 2a. (2). 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. 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 ... Square root in the denominator ; − b {\displaystyle -b}. {\displaystyle -b} ; + b 2 − 4 a c {\displaystyle \textstyle +{\sqrt {b^{2}-4ac}}}. {\displaystyle \ ... The quadratic formula solves quadratic equations. Given an equation in standard form, ax²+bx+c=0, the formula is: x=(-b±√(b²-4ac) ... 2−4(1)(−9)2 ... ... 2 + bxy + cy 2 of discriminant b 2 - 4ac = - d we can associate an ideal of norm a. Then the quadratic form associated to d with respect to this basis is Q ... Proposition 3 d=a+b+c positive integers with b2 >4ac. (i) When a ≡ b ≡ c ... 2+(b−δ)t. 4. ⊕ Z b+δ−2δt+. 4. ⊂ C. 2 . 4/8. 4. CM number fields. Let K be a ... 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 ... x b ? b2 4ac. 2a. , x b ?b2 4ac. 2a . Page 4. 4. Now, suppose b ¡ 0 but b2 " 4ac (meaning that b2 is far larger than 4ac). An example of a quadratic equation ...