Let be the centroid of the triangle formed by the lines 15 x - y = 82 , 6 x - 5 y = - 4 and 9 x + 4 y = 17 . Then + 2 and 2 are the roots of the equation [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let $(α, β)$ be the centroid of the triangle formed by the lines $15 x - y = 82, 6 x - 5 y = - 4$ and $9 x + 4 y = 17 .$ Then $α + 2 β$ and $2 α - β$ are the roots of the equation [2023]

1 $x^{2} - 7 x + 12 = 0$

2 $x^{2} - 10 x + 25 = 0$

3 $x^{2} - 14 x + 48 = 0$

4 $x^{2} - 13 x + 42 = 0$

Ans.
(4)

Given lines are

$15 x - y = 82 (i)$

$6 x - 5 y = - 4 (ii)$

$9 x + 4 y = 17 (iii)$

After solving the equations, we get the co-ordinates as $(6, 8), (1, 2)$ and $(5, - 7)$

So, centroid, $(α, β) = (\frac{6 + 1 + 5}{3}, \frac{8 + 2 - 7}{3}) = (4, 1)$

$∴$ $α + 2 β = 4 + 2 = 6; 2 α - β = 7$

So, required equation is $x^{2} - 13 x + 42 = 0$

Want Us to Email you About Special Offers & Updates?