1. Tardigrade
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  4. Let l be a line y=m x+c which intersect the curve y=x4-6 x3+4 x-1 in 4 points A ( x 1, y 1), B ( x 2, y 2), C ( x 3, y 3) and D ( x 4, y 4) Statement-1: The sum x1(x2+x3+x4)+x2(x3+x4)+x3 x4 is independent of the gradient of the line l. because Statement-2: The sum x1(x2+x3+x4)+x2(x3+x4)+x3 x4 vanishes.

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Q. Let $l$ be a line $y=m x+c$ which intersect the curve $y=x^4-6 x^3+4 x-1$ in 4 points $A \left( x _1, y _1\right), B \left( x _2, y _2\right), C \left( x _3, y _3\right)$ and $D \left( x _4, y _4\right)$
Statement-1: The sum $x_1\left(x_2+x_3+x_4\right)+x_2\left(x_3+x_4\right)+x_3 x_4$ is independent of the gradient of the line $l$. because
Statement-2: The sum $x_1\left(x_2+x_3+x_4\right)+x_2\left(x_3+x_4\right)+x_3 x_4$ vanishes.

Straight Lines

Solution:

sum $=\sum x _1 x _2=0$ as coefficient of $x ^2=0$