Page 17 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

12..QTuhaedorraytiocf EQquuaadtrioatnics Equations eeLleeaarrnn..Ppuunnjjaabb

5. Find m, if Version 1.1
(i) the roots of the equation x2 - 7x + 3m - 5 = 0 satisfy the
relation 3a + 2 b = 4
(ii) the roots of the equation x2 + 7x + 3m - 5 = 0 satisfy the
relation 3a - 2 b = 4
(iii) the roots of the equation 3x2 - 2x + 7m + 2 = 0 satisfy the
relation 7a - 3 b = 18
6. Find m, if sum and product of the roots of the following
equations is equal to a given number l.
(i) (2m + 3)x2 + (7m - 5)x + (3m - 10) = 0
(ii) 4x2 - (3 + 5m)x - (9m - 17) = 0

2.4 Symmetric functions of the roots of a
quadratic equation.

2.4.1 Define symmetric functions of the roots of a quadratic
equation

Definition:
Symmetric functions are those functions in which the roots
involved are such that the value of the expressions involving them
remain unaltered, when roots are interchanged. For example, if
f (a, b) = a2 + b2, then
f (b, a) = b2 + a2 = a2 + b2 (a b2 + a2 = a2 + b2)
= f (a, b )

Example: Find the value of a3 + b3 + 3 ab, if a = 2, b = 1. Also find the
value of
a3 + b3 + 3ab if a = 1, b = 2.

Solution: When a = 2 and b = 1,
a3 + b3 + 3ab = (2)3 + (1)3 + 3(2) (1)
= 8 + 1 + 6 = 15
When a = 1 and b = 2,
a3 + b3 + 3ab = (1)3 + (2)3 + 3(1) (2)

17