Straight Lines
Centroid — Roots of Quadratic
nta_pyq_2023_apr
Grade 11
Question:
Let $(\alpha,\beta)$ be the centroid of $\triangle$ formed by $15x-y=82$, $6x-5y=-4$, $9x+4y=17$. Then $\alpha+2\beta$ and $2\alpha-\beta$ are roots of
$x^2-7x+12=0$
$x^2-14x+48=0$
$x^2-13x+42=0$
$x^2-10x+25=0$
Step-by-Step Solution
Key Concept: Find vertices by solving pairs of lines. Centroid $=(\alpha,\beta)$.
Roots satisfy $x^2-13x+42=0$.
Correct Answer: 3