DeepConic sections

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.5 Parabolas, Ellipses, and Hyperbolas, #46 · Geometry · Conic sections

The roots of … also involve the special combination

This problem is about second-degree curves (conics).

The roots of $a x^{2} + b x + c = 0$ also involve the special combination $b^{2} - 4 a c$ . This quadratic equation has two real roots if $b^{2}______$ and no real roots if \_\_\_\_\_\_. The roots come together when $b^{2} = 4 a c$ , which is the borderline case like a parabola.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.5 Parabolas, Ellipses, and Hyperbolas, #46

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