AoPS.Morrisville

36 Questions
15 Answers

+1

772

1

+143

Inequalities

Given that and find the range of all possible values of
mehr ..

AoPS.Morrisville 20.12.2019

+1

739

1

+143

Quadratics

Let be real numbers such that
mehr ..

AoPS.Morrisville 20.12.2019

0

771

1

+143

Polynomial Roots

Suppose the polynomial

has integer coefficients, and its roots are distinct integers.
Given that and , what is the least possible value of ?

AoPS.Morrisville 14.12.2019

0

767

1

+143

In the complex plane, the graph of intersects the graph of in exactly one point. Find all possible values of .

In the complex plane, the graph of intersects the graph of in exactly one point. Find all possible values of .

AoPS.Morrisville 02.12.2019

-1

1032

1

+143

Parabola

The focus of the parabola x^2 = 4y is F = (0,1). A line passing through F intersects the parabola at N and M. The line passing through F that is perpendicular to line MN intersects the parabola at a point A in the first mehr ..

AoPS.Morrisville 01.12.2019

0

705

1

+143

Func. & Ineq.

Define

and
mehr ..

AoPS.Morrisville 01.12.2019

-1

927

1

+143

Roots Problem

Babette is thinking of a monic quadratic polynomial with real coefficients. She tells you that when she squares the roots of her quadratic, to form another monic quadratic, surprisingly, it is the same as the original. How many different quadratic polynomials mehr ..

AoPS.Morrisville 28.11.2019

0

1278

9

+143

Integer Roots

In a certain polynomial, all the coefficients are integers, and the constant coefficient is 42. All the roots are integers, and distinct. Find the largest possible number of integer roots.

●●●●●●●●●

AoPS.Morrisville 23.11.2019

-1

771

2

+143

Function Eq.

Let S be the set of all nonzero real numbers. Let f : S to S be a function such that f(x) + f(y) = f(xyf(x + y)) for all x, y in S such that x + y 0. Let n be the number of possible values of f(4), and let mehr ..

AoPS.Morrisville 23.11.2019

-1

791

2

+143

Rational Ineq. #2

Let and be constants. Suppose that the equation
mehr ..

AoPS.Morrisville 23.11.2019

-1

785

3

+143

Rational Ineq.

Define

and
mehr ..

AoPS.Morrisville 23.11.2019

-1

919

1

+143

Polynomial Forms

Find the polynomial p(x), with real coefficients, such that p(2) = 5 and p(x) p(y) = p(x) + p(y) + p(xy) - 2 for all real numbers x and y.

AoPS.Morrisville 21.11.2019

0

7

0

+143

Polynomial Forms

Find the polynomial p(x), with real coefficients, such that p(2) = 5 and p(x) p(y) = p(x) + p(y) + p(xy) - 2 for all real numbers x and y.

AoPS.Morrisville 21.11.2019

0

736

2

+143

Optimization Prac.

Let and be real numbers such that . Find the maximum value of .

AoPS.Morrisville 21.11.2019

0

815

2

+143

Discriminant Prac.

For what real value of does the range of the function
mehr ..

AoPS.Morrisville 21.11.2019

0

766

2

+143

Polynomial Forms

Find the polynomial with real coefficients, such that
for all real numbers

AoPS.Morrisville 18.11.2019