book Maths Puzzle Numerical Ability

Shortest distance between two points

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book Other Question

Describe the locus of the points.

Points that are equadistant from the vertices of the polygon.
Does this quadratic equation have a solution and how do I justify?
1. p2-4p+4=0, 2.m2+m+1=0, 3. 3z2+z-1=0