Are there any applications where the precise value of the discriminant is crucial, rather than just its sign?

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 ... However, we know there must be another independent solution. It's not obvious what that might be, but let's make the educated guess y(t) = C2teλ1t. Jan 21, 2020 ... Meoh789 Play Hard Win All The Best Online Games. Apr 2, 2012 ... ... b, and c. To calculate the roots of the equation the program calculates the discriminant D, given by D=b^2-4ac." Then it goes on to give me ... ... 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. (2ax + b)2 = b2 − 4ac. ⇒. 2ax + b = ±. √ b2 − 4ac. ⇒. 2ax = −b ±. √ b2 − 4ac. ⇒ x = −b±. √ b2−4ac. 2a . This is the quadratic formula. 1Jason Zimba is a ... 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 ... Oct 20, 2011 ... (a) Prove that the discriminant D = b2 - 4ac ∈ K has a square root. /. D in L and that we have L = K(. /. D). [Hint: use the quadratic formula ... s = (-b – [b2 – 4ac])/2a. 1. Add them: r + s = (-b + -b)/2a = -b/a. 2. Multiply them: rs = ([-b]2 – [b2 – 4ac])/4a2 = c/a. back. Simplify. Check the solutions. Using the Discriminant, b2 − 4ac, to Determine the Number and Type of Solutions of a Quadratic Equation.