If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$n$$-th power of the other, then show that
$$${\left( {a{c^n}} \right)^{{1 \over {n + 1}}}} + {\left( {{a^n}c} \right)^{{1 \over {n + 1}}}} + b = 0$$$
Answer
Solve it.
2
IIT-JEE 1982
Subjective
$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$ by $$n$$, where $$m$$ and $$n$$ are natural numbers. Two squares will be called ' neighbours ' if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighbouring squares.Show that this is possible only if all the numbers used are equal.
Answer
Solve it.
3
IIT-JEE 1982
Subjective
Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real solution.
Answer
Solve it.
4
IIT-JEE 1980
Subjective
Find the solution set of the system
$$$\matrix{
{x + 2y + z = 1;} \cr
{2x - 3y - w = 2;} \cr
{x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr
} $$$
Answer
$$x = 1,\,y = 0,\,z = 0,\,w = 0$$
Questions Asked from Quadratic Equation and Inequalities
On those following papers in Subjective
Number in Brackets after Paper Indicates No. of Questions