How can technology be used to enhance the learning of the discriminant?

Apr 11, 2018 ... For any equation of the form [ ax2 + bx + c = 0 ] the values of x ( the roots of the equation ) will always be [ ( -b ± ✓( b2 - 4ac ) ) / 2a ] ... If b2 − 4ac < 0, we say the equation is elliptic. Example 1. • The wave equation utt − uxx = 0 is hyperbolic. • The Laplace equation. Sep 12, 2024 ... 2. b2 - 4ac > 0. There are two distinct complex roots α 소 iβ. The general solution is y(x) = α1eα+iβx + α2eα−iβx which can be written as ... 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 discriminant is 0, so the root is rational and the equation can be solved by factoring. In. , substitute: Since. , the equation has 2 real roots. b2 4ac>0. The quadratic formula solves quadratic equations. Given an equation in standard form, ax²+bx+c=0, the formula is: x=(-b±√(b²-4ac) ... 2−4(1)(−9)2 ... 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. 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 ... Jun 4, 2014 ... 3 Answers 3 ... Δ=b2−4ac>0 means that the equation has two real solutions. Δ=b2−4ac<0 means that the equation has no real solutions, but two ... Jun 3, 2016 ... Let λ± = −b±. √ b2−4ac. 2a be the roots of p (λ) and suppose for the moment that b2 − 4ac 6= 0. From Eq. (1.3) it follows that for any ...