Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

Suzi builds L shapes with blocks. An L shape that is 3 blocks high uses 7 blocks. We need to find ho...

Linear EquationsSequencesPattern RecognitionProblem Solving
2025/5/3

The problem asks us to determine the number of solutions and the solutions of the equation $f(x) = 0...

Quadratic EquationsRoots of EquationsIntervalsQuadratic Formula
2025/5/3

The problem consists of three parts: a. Evaluate two logarithmic expressions: $\log_{\frac{1}{2}}4$ ...

LogarithmsComplex NumbersSquare RootsPartial Fractions
2025/5/3

The problem consists of three parts: a. Given a quadratic equation $2x^2 - 4x + 5 = 0$ with roots $\...

Quadratic EquationsComplex NumbersMatricesMatrix OperationsSum and Product of Roots
2025/5/3

The problem asks us to express the fraction $\frac{\sqrt{2}}{\sqrt{2}-1}$ in the form $a + b\sqrt{2}...

RationalizationQuadratic EquationsRoots of EquationComplex Numbers
2025/5/3

The problem consists of three parts: a. Divide the polynomial $x^3 + 2x^2 - x - 2$ by $(x-1)$. b. So...

Polynomial DivisionQuadratic EquationsFactoringQuadratic FormulaRepeating DecimalsAlgebra
2025/5/3

We are asked to solve the equation $\sqrt{2+i} = x - iy$ for $x$ and $y$, where $i$ is the imaginary...

Complex NumbersEquationsQuadratic EquationsSquare Root
2025/5/3

We need to solve two problems. First, we need to find an irrational number between 2 and 3. Second, ...

Complex NumbersIrrational NumbersQuadratic EquationsEquation Solving
2025/5/3

The problem describes a quadratic number pattern $4, p, 11, q, 22, ...$ with a constant second diffe...

SequencesQuadratic SequencesPatternsGeneral TermQuadratic Equations
2025/5/2

The problem asks us to solve the equation $\ln(x+2) + \ln(x) = \ln(x+30)$ for $x$.

LogarithmsEquationsQuadratic EquationsSolving EquationsAlgebraic Manipulation
2025/5/2