If A(1, p2), B(0, 1), and C(p,0) are the coordinates of three points, then the value of p for which the area of triangle ABC is the minimum is

A=1p21011p01=121(1−0)+pp2−1=12p3−p+1Hence, A=12p3−p+1 Now, the minimum value of modulus is zero. Since A(p) is cubic, it must vanish for some p other than given in option (a), (b) and (c).