How is the discriminant related to the concept of convexity or concavity of quadratic functions?

Because the value of b2 – 4ac is less than zero, this equation will not have real solutions. Our answer will be 2x2 – 4x + 5 = 0. If we inspect all of the other ... where both square roots are to be considered when b2 − 4ac 6= 0,. (b) Use the result in part (a) to find the roots of the equation z2 + 2z + (1 − i) = 0. We consider the two solutions in (2) one at a time. With the plus, we get x+ = −b+ b2 − 4ac. 2a. = −b+ b2 − 4ac. 2a......... −b− b2 − 4ac. −b− ... 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. 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 ... Let gcd(a, b, c) = 1, D = b 2 - 4ac. Then as remarked in Mathews ([4, pages 132--133]), then there exist integers #, # such that a# 2 + b## + c# 2 = a ... Detailed step by step solution for k=(4ac-b^2)/(4a) term with B + D. The result is. T. C2 — A2. B2. — D2. 1. V 2 H ~ 2 A H [ A C ( A + C)2. +. BD(B+D)2\. <2>. Now a quantity like (.A + C)2 = 4AC + (A - C)2 may be ... 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; 2 )2 - b2. 4 + c. Quadratic formula: the roots of ax2 + bx + c are -b 소. /b2 - 4ac. 2a . Exponent rules: ab · ac = ab+c ab ac = ab−c. (ab)c = abc a1/b = b.