Question

If $x_{1}, y_{1}$ are roots of $x^{2}+8 x-20=0, x_{2}, y_{2}$ are the roots of $4 x^{2}$ $+32 x-57=0$ and $x_{3}, y_{3}$ are the roots of $9 x^{2}+72 x-112=0$ then the points $\left( x _{1}, y _{1}\right),\left( x _{2}, y _{2}\right)$ and $\left( x _{3}, y _{3}\right)$

• A. are collinear
• B. form an equilateral triangle
• C. form a right angled isosceles triangle
• D. are concyclic

Answer 1

Answer: (A)

$x_{1}+y_{1}=-8$,
$x_{2}+y_{2}=-\frac{32}{4}=-8$,
$ x_{3}+y_{3}=-\frac{72}{9}=-8$
$\because$ Area of the triangle formed by
$\left( x _{1}, y _{1}\right),\left( x _{2}, y _{2}\right)$ and $\left( x _{3}, y _{3}\right)$ is $0 .$
Hence, the points $\left( x _{1}, y _{1}\right),\left( x _{2}, y _{2}\right)$ and $\left( x _{3}, y _{3}\right)$ are collinear.