Suppose thataandbare nonzero real numbers, andthat the equationx2+ax+b= 0has solutionsaandb. Then the pair(a, b)is
(A)(-2,1)(B)(-1,2)(C)(1,-2)(D)(2,-1)(E)(4,4)
2002 AMC 10 B, Problem #10—2002 AMC 12 B, Problem #6—“x2+ax+b= (x-a)(x-b) =x2-(a+b)x+ab.”
6
Difficulty:
Medium-hard
NCTM Standard:
Algebra Standard for Grades 9–12:
Represent and analyze mathematical
situations and structures using algebraic symbols.
Mathworld.com Classification:
Algebra
>
Algebraic Equations
>
Quadratic Equation

The product of three consecutive positive integers is8 times their sum. What is the sum of their squares?
2002 AMC 10 B, Problem #11—2002 AMC 12 B, Problem #7—“Set up an equation to represent the relation.”
Difficulty:
Medium
NCTM Standard:
Algebra Standard for Grades 9–12:
Use symbolic algebra to represent and
explain mathematical relationships.
Mathworld.com Classification:
Algebra
>
General Algebra

For which of the following values ofkdoes theequationx-1x-2=x-kx-6have no solution forx?
(A)1(B)2(C)3(D)4(E)5
2002 AMC 10 B, Problem #12—“Write the given equation in the form ofax2+bx+c=0.”
Difficulty:
Hard
NCTM
Standard:
Algebra Standard for Grades 9–12:
Write equivalent forms of equations,
inequalities, and systems of equations and solve them with fluencymentally or with paper and pencil
in simple cases and using technology in all cases.
Mathworld.com Classification:
Number Theory
>
Arithmetic
>
Fractions

Find the value(s) ofxsuch that8xy-12y+2x-3 = 0is true for all values ofy.
2002 AMC 10 B, Problem #13—“Simplify the given equation.”
Difficulty:
Medium-hard
NCTM Standard:
Algebra Standard for Grades 9–12:
Represent and analyze mathematical
situations and structures using algebraic symbols.
Mathworld.com Classification:
Calculus and Analysis
>
Roots