Question

If α, β, γ are the real roots of the equation x3 – 3px3 + 3qx – 1 = 0, then the centroid of the triangle with vertices 

Solution

Correct option is

(p, q)

The centroid of the given triangle is the point

        

                                    = (p, q

           

SIMILAR QUESTIONS

Q1

A(1, 3), B(3, 7) & C(7, 15) are three points. P is the midpoint of ABQ is the midpoint of BC. Locus of a point R which satisfies (PR)2 – (QR)= (AC)2 is

Q2

If A(1, a), B(a, a2), C(a2, a2) are the vertices of a triangle which are equidistance from the origin, then the centroid of the triangle ABC is at the point

Q3

Given the point A(0, 4) and B(0, –4), the equation of the locus of the pointp(x, y) such that |AP – BP| = 6 is

Q4

Coordinate (x, y) of a point P satisfy the relation 3x + 4= 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is

Q5

The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that 

Q6

Q, R and are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.

Q7

The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 

Q8

OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis

Q9

If px1x2….xi,….and q y1y2,…y… are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), = 1, 2 …n is

Q10

The number of points (p, q) such that p, q Ïµ {1, 2, 3, 4} and the equation px2 + qx + 1 = 0 has real roots is