What is the purpose of the '-4ac' part of the expression b² - 4ac?

The discriminant (B2-4AC) is used to determine which conic section will result. If the discriminant is less than zero we have a circle (if A = C) or an ellipse; 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 ... d=b2-4ac No solutions found Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : d-(b^2-4*a ... b2 – 4ac < 0. No real roots. 4. b2 – 4ac = 32- 4x1x(-2) = 9 +8 = 17. b2 ... If b2 – 4ac < 0 , the line does not touch the curve. It is not a tangent. If ... 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 ... If b2−4ac < 0, change format to linear combination of real-valued functions instead of complex valued func- tions by using Euler's formula. general solution is ... (b) The point P = (1,−1,2) lies on both the paraboloid x2+y2 = z and the ... If a 6= 0 and b2 − 4ac > 0, then y has the form c1eαx + c2eβx where α ... 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 ... where a, b and c are real coefficients. The general solution to such an equation is given by the following formula, called the quadratic formula;. If b2 -4ac ... Feb 22, 2011 ... ... b2– 4ac < 0. We are now able to compute the coefficient of ... if n is sufficiently large, max (a, b) << c, c > 0 and b2– 4ac < 0 ...