Janusz Asked

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

Polynomial Relations

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

Mechanical Integration

To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.

More Polynomial Equations

Stage: 5 Challenge Level:

Here you need to start with $$\begin{eqnarray} a(n) &= &1 + 2 + 3 + ... + n &= & {1\over 2}n(n+1)\\ b(n) &= &1^2 + 2^2 + 3^2 + ... + n^2 &= & {1\over 6}n(n+1)(2n + 1)\\ c(n) &= &1^3 + 2^3 + 3^3 + ... + n^3 &= & {1\over 4}n^2(n+1)^2. \end{eqnarray}$$

These are well known results found in many text books and you will find proofs in some problems on this website. See Picture Story and Natural Sum.

Inequality/inequalities. Simultaneous equations. Manipulating algebraic expressions/formulae. Mathematical reasoning & proof. Geometric sequence. Polynomials. Relations. Summation of series. Creating expressions/formulae. Generalising.

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Janusz Asked

Polynomial Relations

Mechanical Integration

More Polynomial Equations

Stage: 5 Challenge Level: