MathDB

2019 A/NT3: The Annual Polynomial Problem

Source:

1/27/2019

Let

P(x)

be a quadratic polynomial with real coefficients such that

P(3) = 7

and

P(x) = P(0) + P(1)x + P(2)x^2

for all real

x

. What is

P(-1)

?

algebrapolynomial2019

2019 C/CS3: Two Numbers Multiply to a Third

Source:

1/27/2019

How many ordered triples

(a,b,c)

of integers with

1\le a\le b\le c\le 60

satisfy

a\cdot b=c

?

2019combinatorics

2019 G3: Isosceles Right Triangle in an Equilateral Triangle

Source:

1/27/2019

Let

ABC

be an equilateral triangle with side length

2

, and let

M

be the midpoint of

\overline{BC}

. Points

X

and

Y

are placed on

AB

and

AC

respectively such that

\triangle XMY

is an isosceles right triangle with a right angle at

M

. What is the length of

\overline{XY}

?

2019geometry

2019 T3: Equidistant Points on a Parabola

Source:

1/27/2019

Points

A(0,0)

and

B(1,1)

are located on the parabola

y=x^2

. A third point

C

is positioned on this parabola between

A

and

B

such that

AC=CB=r

. What is

r^2

?

2019teamconicsparabola

3

Problems(4)