Are there any practical limitations to using the discriminant, especially for very high-degree polynomials?

... 2 (x + (b / 2a))2 = -4ac / 4a2 + b2 / 4a2 x + (b / 2a)2 = (b2 - 4ac) / 4a2 x + (b / 2a) = +/- sqrt ((b2 - 4ac) / 4a2) x = -b / 2a +/- sqrt(b2 - 4ac) / 2a Jan 21, 2020 ... Meoh789 Play Hard Win All The Best Online Games. ... 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 ... Jun 12, 2017 ... The question asks whether entire parabola is below x-axis. This will happen if discriminant is negative AND the parabola opens downward. The discriminant is 0, so the root is rational and the equation can be solved by factoring. In. , substitute: Since. , the equation has 2 real roots. b2 4ac>0. 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 ... Simplify. Check the solutions. Using the Discriminant, b2 − 4ac, to Determine the Number and Type of Solutions of a Quadratic Equation. Mar 4, 2018 ... Explanation: · ⇒ · + · + · 1 · = · 0 · ← · in standard form. with a=2,b=3 and c=1. ⇒b2−4a ... Summary. The symbol over the b2-4ac is called a 'radical', or a square root symbol; ' ± ' means 'plus or minus'; The DISCRIMINANT is the expression under ... Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots.