Solution set of a quadratic inequality. Let CCR" be the solution set of a quadratic inequality, C = {r € R¹ | x¹ Ax+bx+c <0}, with A E S", bER", and c E R. (a) Show that C is convex if A 0. (b) Show that the intersection of C and the hyperplane defined by ga+h=0 (where g 0) is convex if A+ Agg¹0 for some À E R. Are the converses of these statements true?

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