determine the nature of roots

Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The root..

Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots a..

Summary - i) An expression of the form a 0 x n + a 1 x n - 1 +....+ a n = 0, where n is a positive integer and a 0 , a 1 ,...,a n belong to some number system F, is called a polynomial in the variable x over F. ii) The degree of polynomial is defined as the highest index of the variable x occurring..

Sound is a form of energy. It is produced by the vibration of particles and it travels in a wave-like motion. The number of waves passing a point per second is called the frequency and its unit is Hertz (Hz). The pitch of the sound (high or low sounding) is measured by the frequency. Man can hear ..

Determine if the set of natural numbers and the operation of multiplication form a field. => Yes or No..

Introduction - The Environment is everything which surrounds an organism and influences its life in many ways. It includes physical and biological components. The physical components of the environment are soil, water, air, light and temperature. These are termed as abiotic components. The plants a..

Characters Dicot stem Dicot Root 1. Epidermis a. Nature of the cells Thick walled Thin walled b. Epidermal hairs Present, multi cellular trichomes Present, unicellular root hairs c. Cuticle Present Absent d. Stomata Presen..

Determine the nature of the given series. 3 + 9 + 27 + 81 + ... => convergent or divergent or alternating or none of these..

Determine the nature of the given series. 3 + 5 + 7 + 9 + ... => divergent or convergent or alternating or none of these..

Conclusion - We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method..