Are there any different definitions or variations of the discriminant in different mathematical contexts?

and adding a constant (b/2a)2 so as to make a perfect square: a2x2 + bx + ... If b2 - 4ac is negative this solution will involve complex numbers, which ... 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 ... We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ... 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 ... given the nature of the roots, to find the condition that makes this happen. Find the nature of the roots of 9x² +24x+16=0. a = 9 b=24 c = 16 b2-4ac ... Note: The number b2 - 4ac is called the discriminant of the equation ax2 + bx + c = 0. If the discriminant is negative then the equation has no real solutions. Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. 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 ... Oct 24, 2008 ... (2) Let 4ac − b2 = 0. Using separation of variables, we obtain. Z dy ... b2 − 4ac − (2ad + b −. √ b2 − 4ac)et. √ b2−4ac . (2.7). To ... Reduced forms. Consider a form ax2 + bxy + cy2. , with a, c > 0, and b2. -.