Can the discriminant be used to prove that certain numbers are algebraically independent?

Recall from precalcu- lus algebra that if the discriminant b2 - 4ac is positive, the equation (2) has two distinct ... 2 ) + b(c1y0. 1 + c2y0. 2) + c(c1y1 + ... 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 ... If B2 -4AC < 0, the conic is a circle, or an ellipse. If B2 - 4AC = 0, the conic is a parabola. Another way to classify conics has to do with ... 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 ... x b ? b2 4ac. 2a. , x b ?b2 4ac. 2a . Page 4. 4. Now, suppose b ¡ 0 but b2 " 4ac (meaning that b2 is far larger than 4ac). An example of a quadratic equation ... Jun 4, 2020 ... I wish I could use b^2-4ac>0 to check whether the people are real or not. 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. ax2 + bx + c = 0. might have the arithmetic if statement. if (b * b - 4 * a * c) 10, 20, 30 . Then if the discriminant b2 - 4ac is negative, the program jumps ... ... 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. Mar 4, 2018 ... Explanation: · ⇒ · + · + · 1 · = · 0 · ← · in standard form. with a=2,b=3 and c=1. ⇒b2−4a ...