# Recent questions tagged algebra

Let a, b, c be the roots of the

$x^3-2x^2+x+5=0$

Find the value of

$a^4+b^4+c^4$

Solve in integers the equation

$x+y = x^2-xy +y^2$

Find the ordered pair of nonzero real numbers (p, q) if the roots of the equation

$x^2-qx+p=0 \newline \text{ are the squares of the roots of the equation } \newline x^2-px+q=0.$

Write an equation expressing m explicitly in term of n, if m, n >1 and for all x >0

$\log_n x = 3 \log_m x$

Find the expression that is always greater:

$\frac{a^4+2a^2+4}{3} \text { and } \frac{a^4+a^2+1}{4}$

Find the values of a and b if

$(x-a)(x+2) = (x+6)(x-b) \text{ for all real number x.}$

Given a-b=1, what is the value of

$a^3-3ab-b^3$ ?

What is the sum of the roots of the equation

$(x-1)(x+9)(x-5) =0$

For how many different positive integers n does

$\sqrt{n} \text{ differ from } \sqrt{100} \text{ by less than 1}.$

If a, b and c are the zeros, possible complex, of the polynomial

$5x^3+1440x^2-120x+8, \newline \text{ what is the absolute value of } \frac{1}{a}+\frac{1}{b}+\frac{1}{c} ?$

Two imaginary solutions of

$(x-1)(x-2)(x-3) = (6-1)(6-2)(6-3) \text{ satisfy the equation } \newline x^2+k=0. \text{ What is the value of k?}$

For x > 0 , find the minimum value of

$\sqrt{ \frac{(4+x)(1+x)}{x}}$

$\log_x4 + \log_4 x = 17/4$
$x + \frac{5}{x}$