quadratic relations and functions

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 coefficient of the second..

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 identical. Therefore their corresponding term..

Relations and Functions - In our daily life, we come across many relations such as father-son, brother-sister, teacher-student and many more. In mathematics too, we come across relations such as . A is a subset of B . line l is parallel to line m . number m i..

A relation R is a non-empty sub-set of a cartesian product. A relation is a set of ordered pairs, i.e., R A x B where A and B are two non-empty sets. Domain of a relation is the set of all first components. Range of a relation is th..

Determine whether the relation is a function. => Yes or No..

A relation becomes a function only if _______. => for every input, there are fixed number of outputs or for every input, there is exactly one output or for every input, there are two outputs or for two inputs, there is exactly one output..

from a set A to a set B is a subset of A x B. - A relation R on a set A is reflexive if a R a, " a A- A relation R on a set A is symmetric if a R b b R a. - A relation R on a set A transitive if a R b and b R c a R c. A relation R is said to be an equivalence..

Determine which of the graphs represent a quadratic function. => Graph 1 and Graph 4 or Graph 1 only or Graph 1 and Graph 3 or Graph 4 only..

Find the quadratic function which has the zeros 4, - 9. => f ( x ) = x 2 - 5 x - 36 or f ( x ) = x 2 + 5 x - 36 or f ( x ) = x 2 + 5 x + 36 or f ( x ) = x 2 - 5 x + 36..

Find the roots by graphing the related function of the quadratic equation 1 4 x 2 - 1 2 x - 2 = 0. => 2 and - 4 or - 2 and 4 or - 2 and - 4 or 2 and 4..