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
Tag: Engineering
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
Week -2 | Complex Numbers – 5
Practice problems (MCQ Questions may have more than 1 correct answer) Q-1) Find the value of S, where Q-2) If be 2 complex numbers in the argand plane the n = a) b)|z_2| c) d)None of these Q-3) If , where , find the number of distinct elements in . Q-4)… Continue reading
Week -2 | Complex Numbers – 4
Q-1) Show that Solution: Q-2) If , then find the value of the following series: Solution: Substituting in the equation we have We must remember that to represent a Complex Number in polar form, we take out the modulus from the algebraic form. On those lines we can say Thus the equation boils down… Continue reading