This is an optional module for the students preparing for engineering entrance examinations Q-1) Let be a positive integer such that is prime. Choose for , such that the are not all equal. Also let be a polynomial such that for all . Show that the degree of is at least . Q-2) Let be distinct integers.… Continue reading
Category: Algebra
Week -4 | System of Equations – 6
Practice Problems (MCQ Questions may have more than 1 correct answer) Q-1) Solve the equation in reals . Q-2) If , be the roots of the equation , then the value of is a) b) c) d) None of these Q-3) Let be such that has no real roots. Show that the… Continue reading
Week -4 | System of Equations – 5
This is an optional module for the students preparing for engineering entrance examinations Q-1) Find the number of natural numbers which satisfy the following 2 conditions: a) b) divides Solution: , this is divisible by for any natural number 2. Note that for any number to be divisible by , it must be divisible by its… Continue reading
Week -3 | System of Equations – 4
Q-1) Find all reals x for which Solution : Thus if Now the denominator has negative discriminant with positive leading coefficient – thus it is positive for all real . So & . Q-2) The condition that the equation has real roots that are equal in magnitude but opposite in sign is : a)… Continue reading
Week -3 | System of Equations -3
This is an optional module for the students preparing for engineering entrance examinations Polynomials 1.1 Introduction We have already given an introduction to polynomials in our earlier chapters in this module. For any polynomials & , there exists poynomials & such that with . Note that in this case the degree of can be as well. Thus, … Continue reading