Question

Let $l$ be a line $y=mx+c$ which intersect the curve $y=x^4-6x^3+4x-1$ 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.

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false.
• D. Statement-1 is false, statement-2 is true.

Answer 1

Answer: (A)

sum $=\sum x_1{x}_2=0$ as coefficient of $x^2=0$