Algebra Answers

find the nature of the roots of the polynomial 2x^5+x^3+5x+1

a jogger is running home his distance from home as a function of time is modeled by y=-7x + 8. which statement best describes the function

5 Charecteristics of Hindu- Arabic numeral system

A farmer has 200 acres of land suitable for growing rice, wheat and maize. The cost
of growing maize, wheat and rice is Rs.40/-, Rs.60/- and Rs.80/- per acre, respectively.
The farmer has Rs.12,600/- available. To grow maize she requires 20 hours of labour
per acre, for wheat 25 hours of labour per acre and for rice 40 hours of labour per acre.
She has a maximum of 5950 hours of labour available. If she wants to use all her
cultivable land, all the budget and all the labour available, how many acres of each crop
should she plant?

In the following figure we give the average hourly volume of traffic entering and
leaving a section of a city. Determine the amount of traffic between each of the 4
intersections A, B, C and D.
(Note: The number of vehicles entering an intersection should be the same as the
number leaving.)

Use Cramer’s rule to solve
x + 2y + z =5
2x + 2y + z =6
x + 2y + 3z =9 .

Find the roots of 2x^4+9x^3-9x^2-46x+24 by Ferrari’s method.

Find the value of a for which the polynomial x^5-ax^2-ax+1 has −1 as a root with
multiplicity at least 2.

Use the Cauchy-Schwarz inequality to solve x^3-25x^2-4x+100=0, if we know
that all its roots are rational.

Prove that ((x+y+z)/3)^(x+y+z) ≤ x^x y^y z^z ≤ ((x^2+y^2+z^2)/(x+y+z))^(x+y+z)
Where x, y, z element of N