How does the discriminant determine the nature of the roots?

... 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. 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 ... 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. 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 ... What is the probability that the equation Ax2 + Bx + C = 0 has two real roots? This is P(B2 - 4AC > 0). Note that since A,B,C ∈ [0, 1], if we ... The discriminant, b2 - 4ac, offers valuable information about the "nature" of the roots of a quadratic equation where a, b and c are rational values. It quickly ... 1. Let ƒ(x,y) = ax2 + bxy + cy2 be an indefinite binary quadratic form, with real coefficients a, b, c, and discriminant d = b2 —4ac. 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 ... (Algebra: solve quadratic equations) The two roots of a quadratic equation ax^2 + bx + c = 0 can be obtained using the following formula: b^2 - 4ac is ... The expression under the radical in the quadratic formula is called the discriminant, i.e., D = b2 – 4ac · The nature of the roots of a quadratic equation can be ...