A zero discriminant often indicates a singular point, which is a lack of smoothness. Can you explain this connection?

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 ... ... 2 + q, the graph of y = f(x) has a turning point at (−p, q). • For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. 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 ... Jan 21, 2020 ... Meoh789 Play Hard Win All The Best Online Games. Mar 4, 2018 ... Explanation: · ⇒ · + · + · 1 · = · 0 · ← · in standard form. with a=2,b=3 and c=1. ⇒b2−4a ... B2 – 4AC is the discriminant and identifies the type of conic. If B2 – 4AC < 0, then ellipse or circle; If B2 – 4AC = 0, then parabola ... Jul 21, 2023 ... If a>0 and b^(2)-4ac=0, then the graph of y=ax^(2)+bx+c touches x -axis and lies above x -axis. b = (2siso + ses) (Ved – Ves). c = ses (ses + siso) (Ves – Ved). Taking into account that smax > siso the answer of the sum is. x = {-b - √ (b2 – 4ac)} / 2a. 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 ... Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots.