maximum

256 Questions
128 Answers

-2

126

1

+818

quadratic

Find the value of $c$ so that the quadratic equation $4x^2 + 2x + c = 3x^2 - 8x$ has exactly one solution in $x$.

maximum 21 Agu 2023

-2

88

1

+818

quadratic

Find the value of $h$ such that the quadratic equation $7x^2 + 5x = h + 6x^2 + 3x$ has exactly one real solution in $x$.

maximum 21 Agu 2023

-2

98

0

+818

terminating decimals

Find the number of integers $n$ in the interval $1 \le n \le 120$ such that the decimal representation of $\frac{n}{123}$ terminates.

maximum 21 Agu 2023

-2

122

0

+818

help with parabola

Points $A$ and $B$ lie on the graph of $y=3x^2-5x-3+2x-11$, and the origin is the midpoint of $\overline{AB}$. Find the square of the length of $\overline{AB}$.

maximum 21 Agu 2023

-1

92

1

+818

i need help

Let $B$ be the reflection of $A$ over the line $y = \frac{1}{5} x + 3$. Find the coordinates of $B$ if $A = (1,4)$.

maximum 19 Agu 2023

-2

116

1

+818

help hard geo

I need help with coordinates
The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 50$ intersect in two points $A$ and $B.$ Find the distance $AB$.

maximum 19 Agu 2023

-1

118

1

+818

help with circumcenter

Let $O$ be the circumcenter of triangle $ABC$. What is the measure of $\angle BAC$, in degrees?

maximum 19 Agu 2023

-2

79

2

+818

help polynomials

I cant solve this
Let $P(x) = 0$ be the polynomial equation of least possible degree, with rational coefficients, having $\sqrt[3]{2} + \sqrt[3]{3}$ as a root. Compute the product of all of the roots of $P(x) = 0.$

maximum 18 Agu 2023

-2

119

1

+818

help me plz

Let $f(x)$ be a monic polynomial such that $f(0)=4$ and $f(1)=8$. If $f(x)$ has degree $2$, what is $f(x)$? Enter your answer in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are real numbers.

maximum 18 Agu 2023

-2

115

6

+818

absolute value

Find all solutions of the equation $$|x^2-30x-1|+|x^2+30x+1|=30.$$

●●●●●●

maximum 17 Agu 2023

+818

-1

Do not post AoPS homework.

maximum20 Jan 2025