Home
Class 11
MATHS
The vertices of a triangle are (p q ,1/(...

The vertices of a triangle are `(p q ,1/(p q)),(p q)),(q r ,1/(q r)),` and `(r q ,1/(r p)),` where `p ,q` and `r` are the roots of the equation `y^3-3y^2+6y+1=0` . The coordinates of its centroid are `(1,2)` (b) `(2,-1)` (c) `(1,-1)` (d) `(2,3)`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1

. 1/(p+q),1/(q+r),1/(r+p) are in AP, then

The value of p and q(p!=0,q!=0) for which p ,q are the roots of the equation x^2+p x+q=0 are (a) p=1,q=-2 (b) p=-1,q=-2 (c) p=-1,q=2 (d) p=1,q=2

Find the area of the triangle P Q R with Q(3,\ 2) and the mid-points of the sides through Q being (2,\ -1) and (1,\ 2) .

If the roots of the equation (1-q+p^(2)/2)x^(2) + p(1+q)x+q(q-1) +p^(2)/2=0 are equal, then show that p^(2) = 4q

Find the value of x such that P Q=Q R where the coordinates of P ,\ Q and R are (6,\ -1) , (1,\ 3) and (x ,\ 8) respectively.

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

If p : q = 1(1)/(3) : 1(1)/(2) and q : r = (1)/(2) : (1)/(3) , find p : r

If P -= ((1)/(x_(p)), p ), Q = ((1)/(x_(q)),q), R = ((1)/(x_(r)), r) where x _(k) ne 0 , denotes the k^(th) terms of a H.P. for k in N , then :

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (4/3,3) (b) (3,2/3) (3,4/3) (d) (4/3,2/3)