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
Week -3 | System of Equations – 2
1.1 Graph of a Quadratic equation The graph represened by is a parabola (You can read about it more by going to the link) for all real triplets . While the shape of the graph remains the same, the nature depends on the value of this triplet. Consider the following graph: Fig 1.1.1 This graph intersects… Continue reading
Week -2 | System of Equations – 1
1.1 Introduction In general, let us consider the expression , where is real constant for all and . This is called a polynomial in since it’s the variable, and the natural number , which is the highest degree of in the expression, is termed to be the degree of the polynomial. More specifically, the expression for … Continue reading