If α,βare the roots of the quadratic equation x2−5x+6=0 such that α<β and the vertices of a triangle are A3,5,−2,Bα,β,5,C−1,β,α,then the triangle is

The roots of the equation x2−5x+6=0 are α=2,β=3The vertices of triangle areA3,5,−2,B2,3,5,C−1,3,2The distance between two points Ax1,y1,z1 and Bx2,y2,z2 isAB=x2−x12+y2−y12+z2−z12Hence, the sides of the triangle are AB=1+4+49=54BC=9+0+9=18CA=16+4+16=36Observing the lengths of sides of the triangle one is square of the sum of the squares of  the other twoHence the triangle is right angle triangle.