2

Part of 2024 JHMT HS

Problems(2)

Quadratic with Unique Zero

Source:

Q

be a quadratic polynomial with a unique zero. Suppose

Q(12)=Q(16)

Q(20)=24

Q(28)

quadraticsalgebra2024

Triangles Formed by Intersections

Source:

N_1

be the answer to problem 1.
On square

JHMT

X

\overline{HM}

Y

is the intersection point of lines

JM

TX

\tfrac{TY}{XY}=\sqrt5

and the area of

\triangle{XYM}

N_1

. Compute the area of

\triangle{JYT}