maximum

256 Questions
126 Answers

0

73

0

+818

system

Let c be a real number, and consider the system of quadratic equations
y = 6x^2 - 9x + c - 3x^2 + 17x
y = 5x^2 - 3x - 2x^2 + 10x - 18

For which values of c does this system have:
(a) Exactly one real read more ..

maximum Nov 11, 2023

0

80

0

+818

quadratic equation

Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 4x^2 - 8x + 23$ Find the quadratic whose roots are $a^2$ and $b^2.$

maximum Nov 11, 2023

0

50

1

+818

help algebra

Let a and b be the solutions to 7x^2 + x - 5 = 2x^2 - 3x + 1. Compute (a - 4) + (b - 4).

maximum Nov 11, 2023

0

47

0

+818

need help

Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = x^2 - 6x + 8$ Find $1/u + 1/v$.

maximum Nov 11, 2023

0

62

0

+818

Solve

Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.

maximum Nov 11, 2023

0

65

0

+818

expand

Expand (a + 2)(3a^2 - 2a - 12)(a^2 - 2a + 1).

maximum Nov 11, 2023

0

61

1

+818

quadratic

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

maximum Nov 11, 2023

0

81

0

+818

help algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

maximum Nov 11, 2023

0

54

0

+818

help counting

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
A
RRR
CCCCC read more ..

maximum Nov 11, 2023

0

61

0

+818

linear

Fill in the blanks with integers, and select the correct operator ($+$ or $-$), to give an equation whose graph is the line that passes through the point $(-1,8)$ and is parallel to the graph of $4x + 3y = -8 - x - 15y.$

maximum Nov 5, 2023

+818

-1

Do not post AoPS homework.

maximumJan 20, 2025