Theory of Equations

Some simple problems... more to follow...

Please scroll to the bottom of the post ONLY after you solve all the questions.

(1) If 2+i√3 is a root of x² + px + q = 0 and p,q are real, then

(p, q) = (__, __).

(2) Solve for x:

| x² + 4x + 3 | + 2x + 5 = 0 where |.| denotes the modulus function.

(3) Solve for x:
sin x + cos x = x + (1/x) where x is expressed in radians. Consider only the positive values of 'x'.

(4) If x² + ax + b = 0 and x² + bx + a = 0 have a common root, find the numeric value of (a+b) if a and b are distinct.

(5) Find the number of solutions of the equation:




.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.


All the above questions are previous years IIT-JEE questions! Surprised, aren't you?

Jst fr fn!

Don't you think that I was influenced by today's assembly.

In an attempt to keep the blog alive though I have changed the blog's purpose.