nature of quadratic roots

. A quadratic equation has exactly two roots. For the quadratic equations, we have i) b 2 - 4ac > 0 Roots are real and distinctii) b 2 - 4ac = 0 Roots are real and equaliii) b 2 - 4ac < 0 Roots are imaginary and distinct If the ..

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..

Our investigation reveals that there is a definite relationship between the roots of a quadratic equation and the coefficient of the second term and the constant term. The sum of the roots of a quadratic equation is equal to the negation of the coeff..

Relation between the roots of a quadratic equation - Let a and b be the roots of the equation (i), Then x = a and x = b Since a and b are the roots of the equations (i) and (ii), both the equations are identical. Dividing equation (i) by 'a', we g..

Let a and b be the roots of the equation (i), Then x = a and x = b Since a and b are the roots of the equations (i) and (ii), both the equations are identical. Dividing equation (i) by 'a', we get The equations (ii) and (iii) are identica..

i) The quadratic equations whose roots are a and b is where S = sum of roots and P = product of roots ii) Quadratic equations with real coefficients, the complex roots always occur in conjugate pairs. i.e., a + i b and ..

The number of quadratic equations which are unaltered by the squaring of their roots is => 8 or 2 or 4 or 6..

Differences between a Dicot root and a dicot stem - 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...

In this method of vegetative propagation, a part of the plant, which may be stem, root, leaf or flower, gets detached from the body of the mother plant. The detached part, under suitable environmental conditions develops in to a new independent plant. Among seed plants, vegetative propaga..

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..