See also the
Dr. Math FAQ:
order of operations
Browse High School Basic Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Solving simple linear equations.
Positive/negative integer rules.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- Probability of a Function Having Complex Roots [05/11/2000]
What is the probability that the function f(x) = x^2 + px + q = 0 will
have complex roots when p and q lie between 0 and 1? ...when p and q lie
between 0 and 5? ...when p and q are greater than 0?
- Probate Puzzle [12/15/2003]
A will specifies that every son should receive three times as much as
a daughter and every daughter should get two times as much as their
mother. What is the mother's share?
- Proof of Convergence [09/29/2000]
Why does the ratio F(n+1)/F(n) for the Fibonacci numbers converge to the
- Proof of the Rational Root Theorem [11/13/2000]
How can I prove the Rational Root theorem?
- Proof That 3 = 0? [10/28/2006]
Starting with x^2 + x + 1 = 0 and using algebraic manipulations, I
seem to be showing that 3 = 0. Where am I going wrong?
- Proof That All Numbers Are Equal? [12/06/2005]
I saw a proof that all numbers are equal, which makes math pointless.
There must be something wrong with the proof. Can you tell me what?
- Proof That Equation Has No Integer Roots [05/09/2000]
How can I prove that if p is a prime number, then the equation x^5 - px^4
+ (p^2-p)x^3 + px^2 - (p^3+p^2)x - p^2 = 0 has no integer roots?
- Proof Using Pell's Equation [09/18/1999]
Given Pell's equation for sqrt(D) and p/q = [a1;a2;...;an], can you prove
that p^2 - D.q^2 = (-1)^n.k?
- Proof with Inequalities [10/10/1999]
1. How can I prove that a^6 + 4*b^6 >= 4 if ab = 1? 2. At each vertex of
a polygon, a number is written... How many sides does the polygon have?
- Prove Triangle of Sides with Length... [8/1/1996]
Let a, b and c be the lengths of the sides of a triangle. Prove that the
square root of (a+b-c) plus the square root of (b+c-a) plus the square
root of (c+a-b) is equal to or less than the sum of the square roots of
a, b and c. Determine when equality occurs.
- Pumpkin Price [06/28/2001]
Peter Peter has 40 pumpkins to sell. He will sell them all if he sets his
price at $1.00 each, but will sell one fewer pumpkin for each 5-cent
increase in price...
- Quadratic Equation [6/22/1996]
What is a quadratic equation used for?
- Quadratic Equation [8/28/1996]
What is the formula for the quadratic equation?
- Quadratic Equation [04/08/1997]
The sum of two numbers is 15 and their product is 54. Find the numbers...
- Quadratic Formula [10/01/1999]
Could you give me some ideas for how to use the quadratic formula, and
some practice problems?
- The Quadratic Formula [12/12/2005]
We've been studying the quadratic formula as a way to solve quadratic
equations, but I'm a little confused by it. Can you give me a summary
of what the formula is, how and when you apply it, and why it's important?
- Quadratic Formulas, Equations, Parabolas, Graphing [6/16/1996]
Given 6x^2 + x - 1 = 0, how do I find the roots, the vertex, some
coordinates, and from these graph it?
- Quadratic Formula: Solve for b [08/15/2001]
How do you solve for b in the quadratic formula?
- Quadratic Function [05/04/2001]
What are the effects of changing the values of a, b, and c in a quadratic
- Quadratic Inequalities [03/18/2003]
When I solve (x^2 + 1)/4 greater than or equal to (x + 2)/2 , of my
final two answers, only one works.
- A Quadratic Inequality [4/27/1996]
Solve the inequality: (3x+1)(5-10x)>0
- Quadratic Model [12/03/2001]
The quadratic model S = -17t^2+45t+2570 approximates the number of
suicides by firearms in the U.S. for women, where t represents the number
of years after 1985. In what year were there 2370 female suicides by
- Quadratic Problem [7/12/1995]
Find the quadratic functions with vertex (3,-1) and one x-intercept at
- Quadratic Trinomials [8/14/1995]
How do you factor quadratic trinomials as the product of linear
- Quadrilateral Patterns [03/06/1997]
What is the formula that gives the number of quadrilaterals within a
square grid when you increase the square grid by one unit on each side?
- Quarter Circles [12/20/1996]
Find a function that graphs a quarter of a circle in quadrants II and IV.
- Radical Equation [04/12/1997]
How do I solve the radical equation 3x+(5x^(1/2))-28=0?
- Radioactive Decay of an Isotope [01/05/1998]
I know the decay of the 226Ra isotope involves the use of logarithms (an
exponential function ae^x), but I'm having trouble fitting my information
to my equation...
- Raising Sides of an Equation to the 0 Power [12/04/1997]
If you raise both sides of an equation to the 0 power, will both sides
then be equal to one?
- Raising Sqrt(2) [10/14/1997]
What is the value of x in the following equation: x^x^x^x^x ... = 2 ?
- Rate of River Current [10/31/2001]
Ryan is canoeing upstream while his sister Katie sleeps in the back of
- Rates of Paddling [04/25/2000]
I can travel 12 miles downstream in six hours less than it takes me to
travel the same distance upstream... How fast is this river's current?
- Rational Equations [06/07/1997]
How do you solve 1/(x+1) - 1/(x+2) = 1/2?
- Rational Inequality [2/15/1996]
Find the sum of all values of x such that 6x is an integer and
(x-4)/(x-2) >= 3.
- Rationalizing Denominators [07/12/1997]
How can I rationalize a denominator with odd power radicals?
- Rational Number and its Reciprocal [03/14/2002]
A rational number greater than one and its reciprocal have a sum of 2
1/6. What is this number? Express your answer as an improper fraction in
- Rational Root Test [10/28/1996]
How do you solve the system that consists of the equations xy+6=0 and
- Rational Root Theorem [08/27/1998]
List all possible rational zeros of the each function, then determine the
rational zeros: f(x) = x^3 - 4x^2 + x + 2.
- Ratio of Ratios [06/05/2002]
In a community, 3/5 of the men are married to 2/3 of the women. What
fraction of the residents are married?
- The Ratio of the Speed of a Colonel to his Soldiers [11/7/1995]
A colonel leads a column of soldiers. He marches to the rear of the
column at a speed different from the column's and then at the same speed
marches back to the front of the column. During this time the column
marches a distance equal to its length. What is the ratio of the speed of
the faster to the slower?