What about the case of a quartic polynomial? What is its discriminant, and how does it relate to the roots?

17 In the quadratic formula, b2 − 4ac is called the discriminant. The function f(x) has a discriminant value of 8, and g(x) has a discriminant value of. 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 ... Note: The number b2 - 4ac is called the discriminant of the equation ax2 + bx + c = 0. If the discriminant is negative then the equation has no real solutions. 2 Solving second-order polynomial equations. The roots of the following equation ax2 + bx + c = 0. (1) can be determined as: x1,2 = -b 소. / b2 - 4ac. 2a. (2). If b2 − 4ac < 0, we say the equation is elliptic. Example 1. • The wave equation utt − uxx = 0 is hyperbolic. • The Laplace equation. If b2 – 4ac < 0, then the graph is an ellipse (if b = 0 and a = c, the graph is a circle). Let's investigate it! Open the Quadratic Equations applet: In the ... The discriminant of a quadratic is the expression inside the radical of the quadratic formula. b2−4(ac) b 2 - 4 ( a ... 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 ... ) Suppose that a ~ 0 and that b2 — 4ac ≥ 0. Write the following number as an integer in standard form: ,_b_i/b2 —4ac\2. +b~. )+c. 2a. 2a. 0. Page 5. 6z4 —. 9z3 ... Feb 2, 2020 ... Overview of the discriminant from quadratic formula and its interpretation. Click here to see all quadratic formula videos: ...